I usually have at least $5000 after my initial hires. I've only been playing on Experienced though, so on Insane, I'd probably have to go flat broke.
You don't need a mechanic expert right at the start, and probably don't need an explosives expert either. So what you need or at least want comes down to this:
MD, Spider, Fox are top picks. Doc is probably another good pick for 1.13.
Someone with at least 75 Marksmanship. To train Ira later:
Meltdown, Buns, Grizzly, etc. Lots of picks here. Keep in mind Buns doesn't get along with a lot of characters, Meltdown doesn't get along with Flo, and Grizzly's dexterity is low enough that he'll miss a lot despite his high marksmanship.
Someone with a grenade launcher for 1.13:
Grizzly, Grunty. Don't use any grenades until you are defending Drassen. If you HAVE to, then take Drassen airport early and order more.
An IMP merc.
Some weapon specialization, Body Building, and Athletics is usually the best perk combo, unless you have something specific in mind. Around 55 leadership, 80 marksmanship, 80 wisdom, and a decent enough medical stat to start with a first aid kit.
Preferably someone with something better than a pistol at start:
Many characters. You can also wait on this till MERC opens up and hire either Gumpy or Flo with their premium gear, then give it to a more useful character. It's entirely possible to take Drassen with just pistol users. It's just very difficult to defend it afterwards unless you really trained up a lot of militia.
My usual party ends up being:
IMP, Grizzly, Bull, MD, Mouse
IMP, Fox, Meltdown, Igor, Grunty
But I've done a few other combinations with some success.
Mouse is another character to consider if you don't have Fox. She is stealthy and can come with a suppressed gun with cold ammunition. Letting her potentially kill off a few enemies on a night mission before the battle actually starts. Paired up with Dimitri and you have a shot at taking over a sector without even being detected. Makes the Drassen airport battle a breeze if you can manage it at night. Even if you don't plan on using stealth, her Dex and Agility are top notch, making her a rather flexible character in plain ol firefights.
When attacking Drassen I usually go with the mine first. Train about 10 militia, then take the rest of Drassen. Making sure you have at least 20 to deal with the Drassen counterattack. If Drassen is too much of a pain, you can take Chitzena at the start much easier. For the Drassen airport I highly recommend attacking at night and trying to surround the front entrance from just out of the light range so you have a visibility advantage. For Drassen mine I recommend trying to hole up in the mine foreman building on the bottom left and waiting for the enemy to expose themselves trying to get to you. For the middle sector of Drassen I REALLY recommend having some militia help you, but you can try to hole up in the bar on the bottom, just be careful as one of the enemies has a radio set and will call artillery strikes on you.
Once I take Drassen I order all the following from Bobby Rays:
Armor for Ira, if I didn't already find it.
Ammo for every weapon I have that isn't a pistol. Just the basic ammo types.
Grenades and grenade ammunition for a grenade launcher
2 medical bags, 1 first aid kit, possibly more
Throwing knives for Dimitri
Possibly a utility knife for lockpicking
Possibly another type of knife for Mouse, as well as more cold ammo for her
I then usually hire a cheap mechanic like Gasket to fix some of the 60% condition guns I'm bound to have at this point.
One thing you can do is to go straight to San Mona and look for stuff to do there. From what I can remember, there's about $25000 to be earned there, and a whole lot more to be stolen. Moreover, $15000 of that $25000 can be earned on a daily basis. However it is not necessary. If you wish to liberate Drassen first you can do that, but consider taking the bottom section first, no later than the 2nd day. That way you'll earn a mine income early on. It won't be a lot at first, but it will net you a couple extra thousand by week's end. The income increases the more of Drassen you control, so you should immediately take a 2nd part of Drassen. Just remember that the Queen will send a counter attack to Drassen the moment you are in full control of it. So it can be worth it to just hold onto 2 sections of Drassen for a while and then head to San Mona in the meantime.
As for the counter attack itself. It depends on what version you are playing, like 1.13 for example where you can disable the counter attack. The Queen can send something like 60 soldiers to retake the city, and that early on it's essentially impossible to take on that many enemies at once. However before they attack they will break up into smaller groups and surround the square they want to invade. If you preemptively attack them then, then you have a much easier fight on your hands with only about 20 soldiers. If you're playing 1.13, then consider making your IMP a radio operator. That way he/she can jam radio signals and prevent the enemy from calling for reinforcement/artillery from adjacent tiles.
As for starting mercs. It's worth trying to get some for 2 weeks right from the start because you save a lot of money that way. Don't be afraid of taking some cheap ones: MD, Barry, Grizzly and Steroid are all solid choices (I usually pick them). By the way that's another thing: Blood isn't ideal for healing. You should try to take a team doctor with a high medical skill (and paramedic/doctor trait in 1.13) to heal your dudes, like MD.
I don't recommend turning off the counterattack. It's easily the most fun moment early in the game. I survived it a few days ago with Flo, Grizzly, Biff, Bull, MD, Ira, Dimitri, and my auto weapons IMP merc. Not exactly a heavy hitting team. I had 20 militia and 10 militia came in as reinforcements, and I survived the attack by bolting to the rooftop of the building in the middle of Drassen mine and having my whole squad go prone 1 tile away from the buildings edge while Grizzly used up all the grenades I bought from Devin and the grenade ammunition for his grenade launcher.
The enemy AI doesn't usually try to climb rooftops until all opposing ground level forces are dead, but they will still waste turns trying to shoot targets on the roof that they can barely even see. Letting your militia pretty much mow them down unopposed. Just be careful as the ones farther from the roof can occasionally manage a lucky shot.