So basically, what three $500 guns should you request?
1. Glock 19 - one of (if not the) best "do it all" guns on the market. 15+1 rounds of 9mm, durable enough to take nasty hopped up ammo (ie, the 1300fps Buffalo Bore stuff), big enough to use as a vehicle/home gun, small/light enough to easily carry all day, accurate enough to use for competition, comfortable enough to shoot hundreds of rounds at a time, reliable enough to trust it to go bang when you need it, etc etc. It may not be the best choice for some specific roles (ie, a 1911 has a nicer trigger), but it will do everything you need a handgun to do
Browning Buck Mark/Ruger 22/45 - A quality .22LR pistol is a requirement to have a complete collection. You will shoot this gun more than anything else. You will need to learn proper breathing, trigger control, sight picture, etc..and a quality .22LR is the best tool for the job. Even though the trigger will be different than other guns in your collection, the basics WILL transfer over. I shoot my Glocks better because I train on my Buck Mark. You will too
Rock Island 1911 - It may be a lower end 1911, it may not be the best choice for a carry gun, it may not be as pretty or as tight as some other $2k 1911, but it's still a 1911, so it'll still be fun as hell to shoot. You could get a basic model and mod it to your liking (which isn't very hard to do), or get a "tactical" model and have the basic mods already covered. Rock Island, IMO, makes the best "first" or "starter" 1911
Since you're a bigger guy, you probably don't need a little .380 pocket gun. I'm 6'1" at ~200 lbs, and I can carry my Glock 19 in pretty much any clothing. I tried the whole tiny .380 thing for a while, but I much prefer having something bigger. I won't be going back to .380