The way I climbed the Gallente PVE ship ladder

Thorax
My first love, as soon as I got over the fun of pressing F1-F8 on a Catalyst I settled into this ship for quite a while, it was able to field 5No Hammerhead had a nice armour tank and able to mission the early missions well. It was also where I was first popped in low sec by an Arazu. Later I went back to try to take on a Arazu with a Thorax but to no avail.
Mrymidon
After getting into trouble on some level 3's I managed to save up enough for the next step up the chain - a battlecruiser. Seeing as how 90% of my damage was coming from drones I picked the drone boat and armour tanked it. One of the early skills I brought up to level V was battlecruiser and I nearly never left the Myrmidon. I moved onto to trying out a shield tank on various ships only to find the the Myrmidon passive tank was rock solid and beat the pants of the armour tank for missioning mainly because you don't have to swop out for specialised resists depending on the mission.
Dominix
Shortly after getting the Mrymidon I bought a Dominix and after three missions got it blown apart. It was a valuable lesson and quite a while before I got back into a battleship. About this time I moved into wormhole space and the Dominix was our workhorse, spider tanked with sentries, the Dominix was repsonsible for a lot of Sleeper wrecks.
Ishtar 
This was a long term goal of mine, to fly the Drone Assault Cruiser. Small, hard, fastish (compared with the Domi), it quickly developed a passive shield tank, a single gun (later a civilian gun!) to show the drones what to kill and a drone bay full of nasty hurt. The tank could handle almost anything until I met 10/10 complexes. Up till then I had never added propulsion modules and was happy to slow boat round. After loosing my shields to alpha I started adding speed to my tank. I finished my engineering skills bringing all my shield skills to V.
Astarte
The one downside of the Ishtar was that it didn't do much damage. It would eventually wear anything down but you had to be patient. With BC V and a tendency to fly Brutix for PVP I naturally moved into the Astarte Command Ship. 7 Heavy Neutron Blasters firing tech 2 ammmo with 3 magstabs puts out over 1000dps not including 5 No Hammerheads, not much can withstand that and it's natural resists make it ideal for Gurista space.
The future
At 50 million skillpoints Slay can hardly be considered young. Flying in nullsec has pointed out that there are ships better able to pull in the iskies - faction battleships and carriers. Seeing has how I have never had much money I am going to stay sub capital and improve my base skills. Their are a few end-game PVE ships - the Marachiel seems to be everyones favorite though the Navy Domi or the Navy Mega might suit my skill set better.