Hard to say on the choke question. You can try 2 exact guns with the exact shell and the exact choke and one will work well and the other might not, go figure. The only tried and true method (which can get expensive I know) is to try a couple of different choke / shell patterns. I've worked up a 1/2 dozen guns of all different kinds and you would be amazed (in some instances, not all) how one gun/choke/shell combination will work gangbusters and if you simply switch pellet size (changing nothing else) you won't be able to get a pellet on the paper.

Bottom line, get a choke or two (might buy them used or borrow someone elses from thier gun if it will fit yours) buy a box or two of different shells and go to the pattern board.

Its fun work and you WILL NOT be dissappointed when you get finished.