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Currently, I have notes for builds that combine melee and ranged attacks for all my characters. I got most of my advice from the character creation faq on Gamefaqs where one person has a guide that details what perks to take, what to avoid, and how to set SPECIAL stats, together with my own knowledge. He recommends combining perks for ranged and melee weaponry due to all the extra levels from the DLCs and because we can now max all our skills, something that couldn't be done in the vanilla game.

I have no notes for builds that use primarily unarmed or melee combat. But now that I've been told that hand-to-hand builds are more powerful and viable than I've come to understand.

All of my current build notes have variations for whether or not they use VATS, take Wild Wasteland, or have low intelligence. Also, there are options for each build on whether to use Light Touch and its appropriate perks. Builds not using VATS use Implant GRX and Chemist. Variants that do not have low intelligence get Pack Rat.

Now I've been thinking that maybe I should use either ranged or melee, but not both. Considering the carry weight from armor, weapons, equipment, and other items that I'll be carrying, I'll probably need to cut down the arsenal of weapons I plan to carry.

Unlike Fallout 3, it is not possible to max all stats, and despite the higher level cap, the increased perk rate means you don't get as many perks as you did in Fallout 3, here you only get 25 compared to 29.

Guns: Whether or not to use either Grunt or Cowboy and use weapons that gain an increased bonus to damage from either perk. If not using Grunt, there is the option of whether to primarily use a shotgun or not. If not using Cowboy, Grunts and Non-grunts have the option of whether to use single-shot weapons or powerful automatics. Automatics don't have very high critical chance modifiers and/or deal high critical damage.

Energy Weapons: Choice of using Laser or Plasma. Plasma builds using VATS can take Plasma Spaz. Laser Commander for Laser weapons. Both have options for using single-shot pistols and rifles or automatics. As with Guns, automatics don't deal high critical damage and also have a low critical chance modifier.

Pyromaniac: Can go either melee, unarmed, or use Flamers and the Sonic Emitter Tarantula. Flamers however don't deal very high critical damage or have high critical chance modifiers.

Hand To Hand: Can go either melee or unarmed. Melee needs max Strength for maximum damage. Unarmed as special unarmed techniques. Both have automatic striking weapons as well as single-attack weapons, the former of which are unaffected by Slayer and Super Slam.

Explosives: Thrown grenades, launched grenades, or missiles are the options. In Hardcore, however, the ammo weight of launched grenades and missiles can get pretty high. Together with the risk of getting caught in your own blast radius makes the practicality of this build questionable.

I originally had planned to use both an unarmed and melee weapon together with either Guns or Energy Weapons and some explosives with all my builds. I don't have any builds that use any of the perks that would improve the damage potential of explosives. All of my builds are planned to have endgame Strength, Agility, and Luck maxed. Strength for increased carry weight and melee damage, Agility for maximum reload speed, and Luck for the increased critical chance. All builds also used three hand-to-hand perks: Slayer, Piercing Strike, and Super Slam.

All builds also have one major focus: increased critical chance and damage, increased attack speed, or increased damage outside of critical hits.

Now I'm starting to wonder if this is the best way to play the game. Can someone help me out? Should I focus on only one combat style by endgame and pick the appropriate perks to maximize its effectiveness?
Do whatever you feel like, honestly. Myself, I did one build for all kinds of Guns, one for all kinds of Energy Weapons, and one for Unarmed/Melee weapons. I find each class has various weapons that are good for different circumstances. Never tried an Explosives only build, but it can complement other builds easily.
All my critical builds take Built To Destroy. However, looking at the Fallout wikia weapons table for New Vegas, certain weapons have a critical chance modifier of only 1. Most weapons affected by either Grunt or Cowboy have a modifier of only 1. The weaker Cowboy guns do have a higher chance modifier, as does the Grunt's Light Shining In Darkness, as well as the melee weapons used by both. So I'm wondering if taking the trait is worth it for those two build types. Or if they are better suited as Quickshot builds that focus on increased attack speed, taking Fast Shot and Ain't Like That Now instead of Built To Destroy and Just Lucky I'm Alive.

Shotguns also deal poor critical damage as do many automatic weapons that have a very low critical chance modifier. So maybe I shouldn't bother making a critical build with shotguns and just go with increased attack speed or increased damage per shot with those weapons. And I'm guessing that increasing critical chance through equipment, Finesse, high Luck, and other perks is a bad idea if using Automatics and just go with increased damage outside of criticals as they are unaffected by traits and perks that increase attack speed. Or use them with Light Touch and wear the Courier Duster with the Space Suit Helmet.
Are Explosive only builds practical? Or are they better off as a secondary attack skill for other builds? Would I even have enough perk slots to take all the explosive build perks for use with other builds? What about Melee and Unarmed perks? Would they also be good to fit into other builds? Can you make a build that uses melee and ranged combat, and have enough perks to fit them all? Maybe this would work best for builds that don't use criticals as they have more perk slots than other builds, such as Critical builds using Light Touch and its synergizing perks.

Here's the list of skill perks:

Guns: Hand Loader

Cowboy: Cowboy

Grunt: Grunt

Shotguns: Shotgun Surgeon, And Stay Back

Energy Weapons: Vigilante Recycler

Lasers: Laser Commander

Fire: Pyromaniac

Hand To Hand: Super Slam, Piercing Strike, Slayer, Purifier, Unstoppable Force

Explosive: Demolition Expert, Heave Ho, Splash Damage, Hit The Deck, Mad Bomber

And here's a list of non-combat perks:

Critical: Finesse, Better Criticals, Just Lucky I'm Alive

Faster Attack Speed: Ain't Like That Now

Increased Damage: Bloody mess, Thought You Died

Defensive: Toughness

Light Armor: Light Touch, Travel Light, Tunnel Runner

VATS: Nerves of Steel, Grim Reaper's Sprint, Math Wrath, Plasma Spaze (for Plasma users)

Other secondary Perks: Silent Running, Them's Good Eating, Jury Rigging, Strong Back, Burden To Bear, Pack Rat, Comprehension, Voracious Reader, Educated, Quick Draw, Rapid Reload, Gender Perks

These are all the best perks to choose from, though there aren't enough perk slots available for all of them. That and you sometimes need to choose lower-level perks while waiting for better perks to unlock.

Cowboy, Grunt, and Pyromaniac all affect weapons in both melee and ranged combat, though Pyromaniac also affects certain Unarmed weapons. I would think that Melee only Cowboys or Grunts would be too weak against tougher opposition, such as deathclaws, even with all the appropriate perks.

So would it be a better idea to combine ranged and melee with some explosives? What do you think?
I found from making lists that if you try to make a build proficient in ranged and melee is practically impossible to get all the important perks, meaning you will never reach your full potential in either. Even if you sacrifice other important utility and defensive perks. Choosing all combat perks on such a build wouldn't be very enjoyable or fun without other perks to customize your character. So, I've decided that one style should be built upon only. Traits, perks, and equipment are what help to develop a character. Much more specialization is done here than in Fallout 3.

Maybe if New Vegas had the perk level down to one every level instead of every two levels, it would be a different story.
DwayneA: Maybe if New Vegas had the perk level down to one every level instead of every two levels, it would be a different story.
There's a mod for that I used to run on every playthrough after the first vanilla playthrough. It let me grab the non-combat perks without losing combat progression so I got to see more options in less time basically.

On the whole though I think you're thinking into this too much. You don't even need perks to really make the best weapons viable. The game is really not all that terribly difficult outside of the DLC's where, yeah you should probably have at least one dedicated style developed. Either way the game difficulty is pretty heavily biased in the players favor though so I wouldn't worry so much about optimization as you're functionally only doing it for optimization's sake at that point - which is fine and I highly recommend the perk every level mod for that as it just allows you to push a given character to maximum efficiency sooner.

Just don't get into the trap that anything is really needed. Hell I used to let my combat skills stall out at 70-ish for large portions of the game because speech, science for hacking, and lock picking are far harder checks with more interesting "rewards" to make in general than "hit the target more gooder".
I learned from experimenting with the online planner for New Vegas that even if you find every skill book, it's impossible to max all skills as a low-intelligence character. You need very high intelligence and take certain traits and perks to do so. Since I use YUP, the Skilled exploit no longer works.

And how is it possible that players are able to build upon ranged, melee, and explosives? How do they do it?

As for me, after watching certain level 50 builds that focus on one style of combat on Youtube, maybe I should do the same and focus each build on only one style for specialization for maximum effect.