Are you kidding me? Bombing run, even with the "modified" EXP and GP after the patch before the last one is a horrible way to get GP. Yesterday, I spent a whole HOUR on one game of bombing run, finishing with a 102 - 73 and 1 mission, and only got 341 GP... WHAT A WASTE OF TIME. I bet I could have finished 2 CFs in that time and gotten 2x-3x that amount.
OMA isn't that great unless you are sure that you can get first place every single game, and even then, the GP and the EXP is only decent. Once upon a time, that game mode was the way to make some easy GP, but after a patch back in the day, Nexon decreased the payout considerably.
Elimination is OK, it's what I play most of the time, because there's a much less competitive atmosphere and for 15 minutes of playing, I get typically about 300 GP.
"Shot games" is meant to be shotgun games, correct? I wouldn't know about the payout because I haven't used a SG in about a year...
GP cases is the lazy/rich person's way out of grinding, but it a viable means of getting either crap or a tonnage of GP. If you do buy GP cases, buy at least 15, because there's a good chance you won't get anything higher than 25k if you buy only 7. (I wouldn't know, I haven't spent a single cent on this game.)
In my opinion, having a good team for Elimination Pro (such as a clan with good players) is the fastest way and most reliable way to get GP. The other day, my clan and I went 11-0 on other regular players, and I got 400-some GP for only playing about 20 minutes.
The same could be said about CTF games with stacked sides since as long as you can capture one or two flags with your team backing you up, that equals easy GP.
Another option would to fireteam with experienced players, since as long as people can stay alive, you'll get points that turn into quick GP.
Adding onto Obama/Mouzie's post regarding equipment, I think that it's a good idea to use the HE grenade, because if you play one of the aforementioned game modes, a HE can get you loads of kills and will pay for itself within a couple of games.