Grain refers to the weight, typically of a bullet. There are 7000 grains to a pound. In general, lighter bullets move faster, but will slow down faster, and may not penetrate as much. in 9mm Parabellum (9mm Luger) I happen to like 124 grain.
Standard, +P, and +P+. A governing body of ammo makes called SAAMI establishes standards for ammo. They may decide "4mm Whatzis Auto will have a pressure of 100 kiloTeslas" That is what standard 4mm Whatzis will be loaded to by all makers- no hotter.
However, a higher energy version may be made and marked +P. There are only FOUR official +P cartridges- .38 Special, 9mm Parabellum, 45 ACP, and ALL .38 Super ammo is +P. Other rounds could be CALLED +P, but there is no official consensus on just what that is.
SOME ammo makers came up with a hotter, higher energy load- that is the +P+. There is NO official consensus on just what ANY +P+ would be. Walk away from that- it will not end well.
SOME guns are not made to use the hotter +P loads. While it is unlikely they will explode in a shower of sparks and screams on the first shot, it WILL wear the daylights out of the gun, and shorten its life.
If you are asking my advice on what would be a good 9mm Parabellum cartridge for self defense, would look at any 124 gr jacketed hollow point made by a major ammo company, such as Winchester, Federal, Remington, Speer, etc. Leave the +P stuff alone. Want more power? Buy a more powerful gun.
The MOST important criteria- the ammo that you choose MUST cycle your pistol- feed, chamber, fire. extract and eject 100.00000% of the time. I don't care if it can knock a rhino over- if the danged pistol jams every other shot.
Some notes for you to read-
http://ammo.ar15.com/project/Self_Defense_Ammo_FAQ/index.htm#9mm