I know you are very new to all this BlkBrd, so its kind of like drinking from the fire hose.
The xxx gr statement refer to the projectile weight, the round or cartridge consists of the brass/steel case, the powder, primer and the bullet (or boolit) Most folks shoot Full metal Jacket (FMJ), rounds for practice, they are generally cheaper, but use Jacketed Hollow Points (JHP) for their self defense ammo (more potential for a stopping wound and less potential for a through and through shot I injuring others) However, you should always try different brands and weights to see what shoots accurately and cycles the pistols action (loading and ejecting) This will vary a little from firearm to firearm.
The XDs, Glocks, M&Ps, etc (most of the modern pistols) were all designed with commoly used ammunition in mind, so you won't have much of a problem with any of the major brands.
9mm is less expensive than .40 which is marginally cheaper than .45 so if you are looking to have something you are going to shoot a lot to begin with and are budget minded, 9mm is probably your best option. Plus, IIRC in your intro, you were interested in something your spouse would enjoy also. If she hasn't been exposed to shooting handguns, the 9mm is also a great place to start.
As far as sights/trigger and other mods go, again the pistols above will be more than adequate for you as a beginner. I usually caution against mods until someone learns and becomes proficient in the basics. All the bells and whistles won't make someone magically a good shot if they can't master the basics.
YMMV as I'm no 'expert', just a guy with a little experience trying to lend a hand.
very nicely put, thank you for keeping it simple for dummies! Im so friggin overwhelmed right now that i cant even figure out which safe I need! i have 8 tabs open just looking at safes. i want a fire/waterproof one so i can store some other things...easy, i thought...until i read that they can rust guns, watches and mold papers! WT...lol.
does a higher grain cause more of a kick? or is it the opposite?