My best run has been with the Lobster, but unless the heavy hitters are powered up I find they can leave you quite exposed. The Dreadbound for example can be pretty lethal but needs a decent fire rate/bullet return rate otherwise in a swarm I tend to get overwhelmed, mind you the blade does help in these situations. Most of the time though I stick with the carbine, try and level it up, aiming for decent fire rate and bonus power etc.
Early on I go for broke with the parasites trying to grab as many buffs as I can, it can back fire though, losing me an astronaut/watch for example. Maybe I should behave myself in the early levels too, bit more particularly about what I collect.