you can take any route you like old bean!
none is better than another, and if your on a budget, and its for a bike thats likely to be left out in the rain, then a spares/seconds bin bike is a gooood plan.
the simpler the better 🙂
the only thing to consider is that there is a whole heap of torque inflicted on the drivechain in SS riding (up any kind of incline at least) in comparison to a geared bike.
a cheap wheel should be treated with care.
if its a cartridge freehub unit, you will find there is a single bearing race somewhere along the freehubs length.
i would advise that you put the sprocket ontop/over this bearing.
it prevents lateral forces on the bearings and makes them, the freehub mechanism, and (the most probably cheese) axel last a lot longer in my experience.
i went for a second hand hope xc wheel in the end, with two bearings along the width of the freehub, and another two in the hub, so no worrys about knackereing them.
i pressume you will need a tensioner on that frame?, many types availible, in two categories.
fixed and sprung.
most work just like a mech, infact i know people who just use old knackered mechs, with the high and low stops screwed right in to fix it in one positions.
i prefer fixed tensioners myself, much simpler, less to go wrong, but require a 2 second (literally) looking at every month or so as the chain wears.
if your missing parts, im sure a nosey on here or the classifieds will sort you out…