The polyurethane varnishes sold for consumer use, like Minwax and Varathane, do not rub out evenly to a high gloss like conventional alkyd varnishes do. The commercial cataluyzed finishes used by production companies do, but applying them without the experience and proper equipment is beyond your abilities.
Minwax, Varathane, Deft polyurethane etc, will polish up to a satin gloss with oooo steel wool and wax after they've hardened enough. I usually give it a week or more. You can get a nice looking finish that way, but you won't get that mirror like piano finish with these products. If you let the last coat dry naturally you'll get a high gloss allright but it doesn't look all that good because of dust and other little imperfections that are impossible to avoid. Spraying the last coat, if you do it well, can help give a glossier finish that looks pretty good. But nothing really beats that hand rubbed mirror gloss if that's what you want.
For that I use an alkyd varnish, like Benjamin Moore One Hour Clear Finish. It's a lot of work to get it perfect. You have to build up many coats, sanding very lightly with 400 grit between coats to take out imperfections, before you put on a very level last coat, which you should let dry for at least a couple weeks. Then polish out using the methods you mentioned. Besides the Benjamin Moore I use, there are a few other varnishes which dry hard enough to polish out. Waterlox Gloss is one. Another one is Behlens Rock Hard Table Top varnish. With the Behlens you need to use their own special reducer for thinning rather than standard mineral spirits or naptha. If you can get the Behlen's it's the best. The Behlens uses a phenolic resin and is very hard when fully cured.