If this is an 18" barrel, you may find yourself having issues with your swing, as short barrels do not help you keep your momentum.
Depending on the game, chokes will vary.
There are several games - Skeet, Trap, 5-stand, Sporting Clays, and FITASC are the most prevalent ones in the US, with Int'l versions of trap and skeet popular elsewhere.
Choke constrictions (in 12 gauge) typically run:
Cyl - .000" constriction
SK - .005"
IC - .010"
LM - .015"
M - .020"
IM - .025"
F - .030-.035"
XF - .040"
SK or IC work just fine for Skeet. Trap singles from the 16 yard line will do well with a M. Sporting clays can have such a wide variety, but most targets are within the IC/LM/M range. FITASC is a harder version of Sporting and targets are more in the M/IM range.
As mentioned, the designation on the choke is an indicator of what it is SUPPOSED to be. Different ammunition, different actual bore sizes and mfg. tolerances can vary, so a choke might actual pattern one size tighter or looser. A pattern board with the ammunition you intend to use will let you know.
If your new barrel is somewhere in the 28" range, that will help more than using a short barrel.
Which game are you going to be doing?