My suggestion is stick with the Myron for awhile before you really invest in higher stuff. I guess you could go Grimsnes, but Caldari ships look cooler, have more shields, and extra high slot modules instead of low slot modules. You could use one of the extra high slots to get a CRU module so you get the onboard spawning bonus. Be warned that module is pricey, but if you want to be a dropship pilot you already accepted the ISK investment.

Then of course fit it with everything else you need to survive like hardeners and such. Once you're actually flying though, always play it safe. Fly around far from the action and wait for a few people to spawn in your ship, then quickly bring them over objectives and try to make it obvious you want them to drop from your dropship (that's the point, isn't it?). And watch out for turret installations, these things take you out pretty fast and at the end of the day your ISK investment is greater than any foot soldier's ISK investment so don't feel bad about being over overcautious if they aren't going to do their job and help provide a safe fly zone.