Ships & Modules

You can train for what ever ship you want. Take a look at the market and browse, see what takes your fancy.

Or if you really want someone else to tell you what to do. Go for a Myrmidon it uses the same skills as your Vexor but with more DPS and tank.

Thanks, I appreciate the help.

Realistically, at this point in the progression as a new player, you may consider getting your Cruiser V out of the way and then focusing on getting the core/defense/wep skills up to par.

Far too often new players rush to the "next ship" without the foundation skills. Then when they struggle, they get frustrated and quit. If mission running is what you're interested in then the cruiser with a few months of support skills built up will get you ready for L3's and moving into your first BC hulls.

What he said, focus on the vexor hull class, in other words vexor, navy vex and ishtar.
I once outlined a skillroute for newer players, the most efficient use of SP would be to focus on drones with a memory perception remap.
This is a very heavy investment into drones, but you need drones with everything so it's very worthwhile.
But be sure to get cybernetics 4 or 3 before anything for +3/4 implants.
You take your relevant core intelligence/memory skills to 3 or 4 max, get gallente cruiser 5 and you max the **** out of drones I mean max it hard don't forget heavy drones are not the way to go atm so focus on sentries and light, medium drones.
So drones you max:

drone interfacing, drones, combat drone operations& scout drone operations.

Then you go for: drone navigation, drone durability, drone sharpshooting, sentry drone operations.
(weapon upgrades in gunnery is perception, memory thus best done during your drone remap.)

Also you want to take up all the empire specific drone specializations to 3.
Dont forget to mesh your skills together get everything to 3 before going to 4 if you can dont take one skill straight to 5.
When you have that all taken care of you remap intelligence and memory and finish up core skills, not to forget navigation.
If you are deadset on cross-training you should go for gunnery and stick with frigates.
Or one empires cruisers for your first year get that one empires turret and ship skills maxed on perception willpower, and dive into intelligence and memory for your core skills.

Mainly because dominix is easily achieved, but hard to master (support skill-wise newbie).
By the time he is committed to drones and gallente, he will be sufficiently schooled to make up his mind.
memory, perception remap will take care of drones, which will need to be very high for a decent domi.
He will have all the ground work for a domi and to not suck.
Myrmidon can become a real SP sink over an ishtar, and a navy vexor has considerably higher dps then said myrmidon.
Especially with drone skills, as low sp gunnery is silly.

Note that all of the above assumes that you are planning on missioning for most of your eve career. I highly recommend trying multiple professions, (exploration, trade, industry, pi, missions, mining, piracy, FW, or some of the less reputable things) before you make a choice of what to fly. If you like drones all of the above suggestions are good, if you like blasters, you may want to look at a brutix instead (decent wormhole ship too!). The suggestions to train your core skills while still in a cruiser are very good for any pve though. If you are at all interested in pvp, I recommend dropping down to frigates, the incrusus is a beast.

Don't rush into the next ship right away. It will perform subpar and you'll find yourself having to backtrack anyway.

Spend time perfecting the current ship you are in and putting it to it's maximum potential.

If you plan on continuing the Gallente Drone boat path definitely focus more on drone skills which will come in handy rather than hybrid gun skills. The standard Dominix doesn't get Hybrid bonuses, and neither does the Myrmidon. Eventually hybrids are nice on the Ishtar and the Navy Domi, but for now T2 drones will be much more useful than T2 hybridd.