Warfare & Tactics

Catalyst > Vexor > Ishkur (optional) > Myrmidon > Ishtar (optional) > Dominix > Rattlesnake

The Gallente droneboats really shine in most PvE activities and offer versatility that few other ship can match.

And because I'm feeling nice (and over-caffeinated) I'll run down the list I provided above...

Catalyst = Not a droneboat, but it offers a good start for a budding Gallente PvEer due to its mobility and damage potential. Fit railguns and "kite" the NPCs at range until they are all dead.

Vexor = A true "droneboat." It can fit a large number of drones and gets a bonus for using them in an offensive role. As a result, you can fit the ship purely to absorb incoming fire and/or do "utility" stuff while the drones do all the damage. Be sure to equip at least one gun to your ship so you can pull NPC aggro before sending out your drones (drones don't like being hurt).

Ishkur = A tech 2 frigate that takes a bit of time and training to get into (it's faster to get into Tech 1 cruisers). Now you might say, "why would I want this ship as its stats are 'inferior' to the Vexor." Simply put; it's small and mobile (if you brush up on the game mechanics, you can "avoid" damage from larger NPCs by simply being fast). Coupled with the fact that it can rely on a full "flight" of light drones (i.e. it can field 5 small scout drones) to do all the damage, you can fit for "exploration," go into "hazardous" places (e.g. low-sec), and avoid most hostile situations.

Myrmidon = Take everything about the Vexor and upgrade it. It has a vastly greater ability to absorb damage, dish it (via its 6 turret slots), and can be fit a myriad of ways. The only penalty you pay is that it is quite slow (even with an afterburner equipped).
If you are looking for a "cheapo-all-in-one" package, this is the closest you will get.

Ishtar = Again, it's a beefier version of the Vexor but carries a [much] higher price-tag, has higher "skill requirements" to use properly, and won't be quite a "tanky" as the Myrmidon (due to limited CPU-Powergrid). However, you can launch 5 heavy/sentry drones ("battleship class" dones) and remain very mobile.
In short, it is a larger Ishkur.

Dominix = Effectively the "king" of armor tanking droneboats. It possesses a very generous drone bay, offensive drone bonuses, can field 5 heavy/sentry drones, and can fit a tank that can absorb the damage of almost all missions.
You can fit big 'ol guns to it to supplement your drones' damage at range, helping you complete missions/plexes that much faster. Or equip remote repair mods to keep your drones alive.

Rattlesnake = Take the drone fielding abilities of the Dominix and add on of the biggest passively regenerating tanks in the game... and you are left with a ship that can pull in as much NPC aggro as it wants, launch drones, and AFK the mission laughing.
The problems with this ship are that it possesses a hefty price tag and requires skills that deviate from the general Gallente philosophy of guns and armor (it requires shield skills and cannot fit turrets, missiles only).