So, you want to be a healer, eh? In EVE, it's called remote repairing or spider tanking when there's a group of them. Saying "healing" gets people all riled up, almost as much as wanting to "join a guild".
Now, healing comes in two flavors - remote shield boosting and remote armor repairing. Former is not used in practice. Reason for that goes like this: healing only works in groups (doh), healed ships still need tank gear (resist modules, shield extenders/armor plates).
On to ship choice: the ultimate healer ship is a carrier. Mostly because it has the largest healing throughput and massive tank, so it's the only healing ship that gets used in the big important 0.0 battles. Even then, it repairs POSes most of the time, which is almost as exciting as mining. Though there are big spider tanking fights now and then. Gallente carrier (Thanatos) is one of the two (other being Archon) that are actually useful. If you check ship bonuses you'll see that Minnie one is the only one that has them focused on remote repping, but it has crap slot layout and thus poorer tank.
For Gallente the Dominix and Oneiros are used for remote repairing, as Sin and Eos don't have any bonuses for remote repairing. Also, they're too expensive for mere mortals to be used in on the front lines, especially as you don't need to keep them in combat for their primary roles (porting stealth bombers/recons around and giving gang bonuses, respectively).
The Oneiros has a couple of good points one is the ship's bonus for armor repair bots. With it at the maximum, med. armor repair drones do 56 HP/5 sec. Considering that medium drones fly faster than heavies (so they can start repairing a ship sooner, which is a general drone problem) and take less damage, they are not that shabby compared to those on Dominix. The only problem is that Oneiros doesn't have the drone bay for spares.
The other is that Oneiros (and all other logistics) can run large repairers/shield boosters thanks to ship bonuses. Of couse, you need to ensure that you have enough capacitor to keep the larges running. You can make Oneiros cap stable with decent armor tank, 2 ECCM and 3 large remote armor reps. Oh, you'll need that ECCM, as you'll be primary not only for incoming fire, but also for all the jamming.
Dominix is a cheaper, more versatile healer. You don't get those nice remote rep bonuses you get on Oneiros, but you can fit for some damage, provide other utility than healing from drones and won't be such an obvious primary target.
Anyway, remote repping gangs are flavor of the month (year?), so a "healer" should be welcome in a lot of PvP corps. And if you'll need ISK down the line, you can get second account, train it for a damage dealing, armor tanking BS and dual box through pretty much any mission or complex.
(Work in progress - rest of the races to come).
