Might As Well Change The Rings And Bearings

Some dirty pistons doesn't mean you need to change the rings. The soot can be caused by a rich condition or even leaking valve seals. How much of a wear-ridge do you have? Was it burning any oil or suffering from a lot of blow-by? If no wear ridge and it wasn't burning oil, I'd suggest you put it back together. As you already know a compression test is a good idea before pulling things apart.

As for what to order, if you're changing rings & bearings, you'll need to measure for what you need, and likely have to have the block (and crank) machined. If there's significant wear you'll need an over-bore and oversized pistons / rings, so the machine shop will need to tell you what needs to be ordered.

I don't recommend just slinging some new rings on existing pistons without having the engine machined. If you measure everything and it looks good (bores are even and tolerance are good), you can get away with it provided you can clean the ring-grooves properly. I definitely don't recommend new bearings on a crank that hasn't been machined. I did that once when I was younger, and created a mess. Again, once it's machined (or you buy a remanufactured one) they'll let you know the bearing undersize that you'll need.

While you're there, you'll need a complete engine gasket set, a timing set, and oil pump as minimum recommendations. I'd suggest a good book on engine building. Bolting on the parts is easy -- the difference between a quality rebuild that lasts many thousands of miles and a ticking time-bomb is proper measurement and selection of parts. You might note that it may be cheaper to just pick up a short-block than to buy the parts yourself, especially if you're new to rebuilding.