If you are looking to buy a complete upper, make sure it doesn't have a flash hider or a bayonet lug and you are NJ compliant.
Another option if you don't want to neuter a perfectly good complete upper is too simply build your own upper how ever you like. You get to build it how you see fit, barrel length, shroud/rails, brake.etc. More people build lowers then uppers, but it really isn't difficult at all just follow the build guide.
But if you want to keep it cheap I would order something like this grind off the lug and replace the A2 FH. That will be about as cheap as you can get.
As far as building your lower before neutering your upper, it depends on how much of a nervous Nelly you are. As DeerSlayer pointed out, there is some dumb law about intent or something, but I've never heard of anyone being charged with it, nor have I heard reports of LE raiding someones workbench looking for flash hiders and bayo lugs. Also as DS said, if you are worried about being raided for having a lower and an assault bazooka upper, buy whatever upper you like and have it shipped to your gunsmith for compliance work.