basic rebuild ... possible?
Any time you change out rings, you must hone the cylinders! The cross hatching from honing helps keep oil on the cylinder walls to lube the skirts and rings. If all you want is a super cheap rebuild and have no racing in mind, you can buy a ball hone from NAPA and hone it yourself on the engine stand, using copiuos amounts of WD40 to lube the hone. If you go this route, be sure to strive for a 40 to 45 degree cross hatch.
All this assumes that the piston skirts are not trashed, and you don't have a nasty ridge in the top of the cylinder. The only way to know if you can go this route is to tear the engine down and inspect for bore taper and skirt to cylinder clearance.
You should replace all bearings too and check the clearances with plastigauge. Replace the oil pump with a NAPA standard volume pump and don't forget to clean out the pump pickup! You'll be amazed at the crap stuck in the screen.
As far as what the heads might need is a shot in the dark without inspecting it. If the guides aren't bad and the heads aren't cracked, you can de-carbon the head and valves and lap the valves in. Don't forget new stem seals.
Inspect your cam. You will most defintely need a new timing chain. If your original cam looks good (which I seriously doubt), you can get a cheap double roller from Summit.
You should be able to pull this kind of rebuild off for well under $600 (I didn't check prices on everything so don't shoot the messenger!) Assuming you don't need valve guides and valve job (which you probably do), won't need a bore and hone (which you might), and that your crank and rods are re-useable without machining. You might get 20,000+ miles with this kind of rebuild and I've seen them go longer with quality oil and maintenance, but there is no substitute for doing it right the first time. Fishy is right about the torque converter. The 318 is internally balanced and the 360 is externally balanced. The 360 will require a 360 style harmonic balancer and torque converter.
Good luck! :)