I've been playing PA recently. My current strategy is as follows:
Get two military labs and rush Skiprays. Your starter capital and the base frigates can both hold them so it's really a good investment. From there I grab Vindicators and resupply stations. About that time you should have a few planets up your sleeve so Trade Ports are useful to boost credit flow. Start getting the weapons upgrades around this time as well. Grab Dynamic Automata upgrade and shoot to Secutors. Automata is probably one of the best upgrades in my opinion, free ship supply and decreased fleet upkeep is never bad. Between the Trade Ports and the Corporate upgrades you should be rolling in the dough in no time.
The backbone of my fleets are Venators, Acclamators, Vindicators and Procusators. Capital ships should be primarily Secutors and ISD II. Despite how beautiful they are don't go overboard on Praetors: they're good ships, but rather pricy. However, having at least one in a fleet is a good idea as they are great sponges to protect your fragile cruiser/frigate force. Corporate command centers are fantastic little things as well, don't overlook them.