I've got an Assault Ship myself, and it just floats along leaving wreckage in its wake.
For Shields, you can either go Hull Tanking with BiWeaves, or go for Class-A shields with Boosters. I've found just the BiWeave and then replace your Cell Bank with another Hull, and it runs like a treat. You can now swap out all Boosters for Chaff and you are rocking. The Hull keeps you in great shape, and the BiWeaves go up and down constantly. This opens up your available power for some MUCH better weapons. Pulses are nice, but a pair of Large Bursts with a pair of Railguns will destroy just about everything. Lasers for anything Asp size and smalller, and the rails will poke out the power plants of anything big. Every half-hour or so I pop back to the station to repair, rearm and cash in bounties.
For PvE I do suggest the Kill Warrant Scanner, as it will significantly boost your cash for bounties.
This is mine:
http://coriolis.io/outfit/federal_a...a2a0000020lB22d2b290d2f.Iw18cQ==.EwBhEYy6a8g=
(except that I put in Military Grade armor as well) I've spent many hours in HighRES and compromised nav points, and have yet to be taken down.
I also do not bother with cargo - an Assault Ship has little room for cargo, and a terrible jump range. Mine is almost exclusively combat, and I have other ships for other purposes.