A .22 would be the best to start, aside from that....
Get whatever fits your hand the best, and look up the rules to whatever competition you want to shoot.
The M&P is not far off from the glock as far as popularity goes. The sig and beretta are both DA/SA which is sub-optimal for competition, but that doesnt mean you cant use it. The sig also has a somewhat high bore-axis for my liking.
Heavier is better for general use. It helps negate recoil like you said, but its bad if you have to carry it a lot, and its bad if it is so heavy that it wont meet the required weight for whatever competition you are shooting.
Your best bet is to handle and preferably shoot a bunch of guns, and simply buy the one that works the best for you.
For example, I like glocks a lot, but I naturally shoot M&P's faster.