no ...you don't have to run a different computer. It's just a tune! You can flash the stock ECU with a tune that'll run the thing just fine using a handheld and a mail order tune. It should be able to start and run the engine without a tune but I like to apply at least a base tune before the first fire up (the 4.6 factory tune won't idle a 5.4 well) if at all possible and then take it in to a dyno for final tuning. You can use coil packs to light the fires if your car is a 96-98, you don't need COP.
As for doing the 4v, it's a good bit more involved than just swapping in the bottom end and slapping your existing 2v heads on it. The power returns tend to be worth it but simplicity is out the door on that and cost goes up almost double.
My strategy has been to start with just ported 2v heads and hot cams, then I'll upgrade later on to the Trick Flow 2v heads or a set of hogged out 3v heads. I've got longtubes being made for that setup. HPS is considering doing a 3v intake based on the 2v intake as well which would make for a simple bolt in 3v upgrade and the potential for lots more top end. I had originally planned on going 4v but the flow numbers from the TF heads and ported 3v heads are close enough that I'll take the weight/cost/complexity savings and use nitrous to make up any difference.