Once you buy any ship in C-Store it is put in your inventory or straight into your list of owned ships. You don't then have to use dilithium.
I've played this game since the original launch. I can tell you that the Dreadnought is a tank. The phaser lance packs a huge punch, and it can equip cannons. Unfortunately the terrible turn rate means that, for most enemy ships, you won't be able to line up a forward attack run. In my opinion the dreadnought is a bit overpriced. If you are a tac. and or have been using escorts, I'd go with the Prometheus. Just load it up with cannons and have a hull repair and shield boost as traits in your engineering slot.
Hope this helps
