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So I've tried playing this game before but I've always been turned off by trying to read up on the game systems and optimize my character, which led to me be being burned out before I even really began. So my question is, how forgiving is this game if one approaches it by just picking skills and abilities based on what sounds cool at the time. I'm planning on playing a talk-y gun-slinger type character, if that's of any importance.
Not very. The game is actually pretty easy, although I'm sure you'll get confused at times.

But honestly, you should have no problems just "winging it".
Although if you would like suggestions about being a gunslinger/diplomat, there's a thread on that:
My first time I read the manual but not much really sank in. I winged it. I made a barbarian fighter with a bit of blacksmithing tech to make my own gear, and I kicked ass all through the game even with crap companions like Jayna Stiles and Virgil with his healing failing on me constantly. Left the combat on real-time the whole time. Persuasion and charisma were somewhat lacking but nothing that made me feel like I had failed.
Yeah, a melee character will be really easy, if a bit boring. Add in some tech skills to make it a little more interesting. Dexterity is the most important stat as it gives you more speed (i.e. more action points per turn, if you play in turn-based mode). Strength gives bonus damage to melee, intelligence will let you learn tech skills.

Once you've played a bit and learned the mechanics, you can try building a more interesting character. A great thing about Arcanum is that nearly any build is viable, which means it really supports roleplaying specific kinds of characters.
The "easiest" plan involves a magic (or at least a non-tech) character, touring the world with Virgil and maybe a couple of others, while playing in turn-based mode.

Just be aware that as part of the main storyline, Virgil leaves you at one point, and then if you want him back you have to hunt down where he went.

But the beauty of Arcanum, as others have already pointed out, is its flexibility. Just about any build can work; though some of the wilder ones will benefit from a more thorough familiarity with the game.
I should probably add that, as Luckmann mentioned, you'll definitely get confused a few times. There's some weird interface design, a lot of abbreviations and stats that are not clear unless you look them up, and things like that. But as long as you're OK having the manual around for reference (searchable PDF helps a lot!) you won't have too much trouble. Also feel free to come back and ask questions in the forums.
Cool, thanks for the responses.
Magic can work, meele with a little extra is just ridiculously easy going but when I first tried a technical gunslinger I had huge troubles and the gameplay got a bit... tenacious.