He told me I should be looking for 9MM Luger rounds, but I was on line and noticed there were some differences for those as well and I didn't know what that other specification meant. Oh well, I'll keep circling and hope for the best.
Sorry for the "novel", but hopefull it will clear up any confusion you have.
You are looking for any of the following: 9x19, 9mm Parabellum, 9mm NATO, or 9mm Luger. They are all the same thing. Now, 9mm NATO is slightly higher pressure than standard commercial stuff, but I can't think of a single pistol (in good condition) made for, say, at least 50 years that would have any noticeable problem with it.
Loads labeled as "+P" are commercial loads at higher than normal pressures, but it is still a recognized standard that should be safe in the vast majority of pistols, although it is higher pressure than even the NATO load and it is best to confirm with your pistol manufacturer that it is rated for +P use. You won't see this on plinking ammo, only SD loads.
Anything labeled "+P+" or something to that effect is loaded beyond recognized pressure standards for the cartridge and the specifications can and will vary from manufacturer to manufacturer. Chances are that it is still safe in most guns, but most (if not all) gun companies don't recommend them and, for me personally, I've never seen or read any verifiable benefit that warrants the extra wear on my guns and the extra recoil. You definitely won't see any plinking ammo loaded to these pressures and only a few SD loads that I can think of go this far.
Once all that is out of the way, the only (important) variables are bullet weight and type. FMJ, TMJ, or "Ball" (today) all refer to lead bullets encased in gilding metal jackets, hence "Full (or Total) Metal Jacket". These are going to be the default for factory loaded practice ammo. They are sometimes further classified by the shape of the tip; Round nose (RN), flat point (FP), or truncated cone (TC) are common. Hollow points are, just that, jacketed bullets with cavities (hollows) in the tip, that are designed to expand on impact. These are more expensive, generally, and are typically reserved for SD or "carry" ammo. There is lots of data and opinion about which ones are best, but generally, a quality "bonded" hollow point from a known manufacturer is good default.
As for weight: most 9x19 loads will be 115 grain (gr) or 124 gr and virtually all of your range ammo will be one or the other. (115 gr was the original weight for the cartridge while 124 gr is the current weight for NATO standard loads) Generally, pick the one closest to your chosen carry ammo in weight and velocity for practice. Right now, take what you can get. SD loads will go as high as 147gr and some boutique loads will go lower with "exotic" bullets. I generally recommend a good hollow point in either 115 gr or (preferably) 124 gr, at either standard or +P pressure (depending on the specific load, the shooter, and the pistol), however some folks swear by 147gr loads. (I don't personally like the ballistics on those, and they tend to offer the heaviest recoil but your mileage may vary.)