Fitting skills will be among the most important of the skills to have outside of the obvious ones of being able to put the large guns/missiles and repairs on.

Engineering will give you more grid and electronics will give you more cpu. Large weapons take a large amount to fit and lacking these skills will help. If more help is needed look at weapon upgrades and advanced weapon upgrades as being on the important list.

Whatever ship you are flying (unless you've got an uncommon passive shield tank fitting) you will be slurping cap. Make sure you can run reasonably for as long as you can. This means Energy Management and Energy Systems Operation as higher priority skills. If you are flying Amarr or Gallante (or a rail caldari battleship) you will also want Controlled Bursts at some reasonable level (not as critical for drone boats such as the Dominix that have drones as primary damage dealing).

As mentioned, drones are important for taking out smaller ships. Being able to send out 5 drones at once to make short work of a scrambler is important. If you are flying a Dominix, you will want your drone skills as high as possible, and the Gallante Battleship skill high too (stacking drone damage bonuses nicely).

You should also be able to run a T2 tank for PVE. T2 resists are very nice, but not on the critical part there (T2 gives 55% resists rather than 50% resists). However, there is a significant difference in Large Armor Repair II (800 hp/cycle) and the meta 4 version (720 hp/cycle). Similar advances are present in shields. Wherever you are (unless you are running with a logistics alt) you will enjoy having a better tank and many times it will mean the difference between a 'leisurely' pve fight and running away to repair structure at the station.