Wow, that's quite a list of potential games right there. It seems like the overwhelming consensus is that either Fallout, Gothic, Master of Orion, or Might and Magic would be good fits for my first purchase. I'm going to really have to give this some thought.
Thank you so much for the groundswell of support and advice! You really are a fantastic community.
P.S.
I have an IBM Thinkpad from circa 2006. Gothic looks like it might be a bit intensive on my aging computer.
Do any of those games require all that much in the way of hardware?

Simon the sorcerer 3d!
Why's everyone looking at me like that? Okay okay, how about broken sword 2? Don't worry, it washes out of your clothes and hair...

Outcast is worth the GoG buy

Well, first off, welcome to GOG. Now for some game recommendations:
Fallout: One of the classics, you CAN NOT miss it.
Outcast (I've heard great things).
Bloodrayne: Decent gameplay and graphics, plus vampires in their best.
Soldiers: Heroes of WW2 (Most UNFORGIVING RTS I've ever played.)
And lastly, since The Joe hasn't popped in yet, The Guild Gold. (It will take over your life, trust me.)

Now now how can you all forget warlords battlecry 3?
Warlords battlecry 3: a rts that leads you make and build a hero like a rpg.
Lead the armys of the dead be it by your sword arm,magic or other useful skills.Destroy the paladin orders!reanimated the life less bones of the dead in to skeletons. destroy your enemy's with unending hordes of the undead.summon demons and devils to aid you.Turn it form day to night. Find rare magic items to help your hero. destroy any who dare to stop you.hire sell swords to aid you in a quest.

Oh no it guild not!
Try Betrayal at Krondor, if you like TES' ers. Up on top of all already listed.
Gothic should work, but probably not on top specs. Couldn't know for sure, thou.

If you like turn based strategies and dark, heavy climate buy disciples 2, this game is fantastic, i actually prefer it over Heroes of might and magic. Altough battles are extremaly simplified its impossible to win them without proper planning.

I think you would like Fallout 1 and 2. Those were my first games, though I've never played tactics. It might be worth checking out as well. I also recommend Gothic 2

You mean girls in their best.

If you're considering Master of Orion, also consider Master of Magic. I don't know how the two compare, but I spent hundreds of hours on Master of Magic back then, and I still play it now and again.
If you're in for an open-world RPG, Fallout of course goes without saying, but the Might and Magic 6-pack has only gotten a bit of a mention yet. Even if you find the first two games too dated, $10 is a paltry sum for the rest of the set. MM3-5 in particular are among my favorite party crawlers.

No, because this vampire game at least is better than Twilight...

Gothic should be fine (tweaking is available and there's some tips in the config for it), and the rest easily. Play Gothics in order. Incredible RPGs. Just be warned they're unconventional (that's why we like em), and you'll want to investigate the control scheme before playing, otherwise you may be turned off. You'll grow to love it quite possibly.
PS. Welcome. Enjoy your stay. :)
I'm sincerely surprised you play anything other than M&M. :) Good good.

Hey, Fallout 1 always felt like an extended prologue to the second part; too little content to bite; not enough dialogues, not enough options, not enough details...

But without prologues, stories are incomplete! Besides, I liked less content. Fallout 2 became boring to me after a while. But it did have as many options and details as the second part, just not that many ... places with them.