Coffinmaker = Best TP'ing gun due to r.acc/damage. It's great gun for quickdraw (but not best). It's the most well rounded gun and a important factor is it's free. Also has great looks.
Martial Gun = Great WS gun for events where you don't need as much R.Acc or if you have a large amount of R.Acc already for tping. It'll make sure your WS due far more damage and/or are very acc. Also works great if you have Joytoy to tp with.
Corsair's Gun (+1) = Best Quickdraw spam gun as it has the highest Base Damage Rating which effects Quickdraw damage.
Hope that clears things up. I have all 3 for my Cor. They're all useful.
To Oberron - You're wrong on the martial gun not adding damage to WS. Read my posting again. I mentioned it add R.acc and/or Damage to WS. You assume right off I'm only talking about Slug Shot and you didn't take into account that Cor can use Detonator and Leaden Salute as well which are WS that TP increases Damage and what's SW have to do with guns?
Definitely "the" gun to have for a Corsair, just make sure u have the patience to unlock it.
if not and u have C rank in aht urghan get urself a Shark Gun, stats on it are good, but second to Coffinmaker