I haven't built this exact setup but I'd be surprised if it all doesn't just plug and play. The RSX brifters have a good reputation and are somewhat easier to overhaul if needed than the later models. The 93 crankset if a wonderful piece and should work fine with a 7 speed chain. You can squeeze a 126mm hub into a 120mm frame but if you have the tools, I'd cold-set the rear so you can re-align the dropouts to the new spacing. Non-parallel dropouts are a recipe for broken axles IMHO. If you want to replace the RD be aware the dropout is different than the modern standard. There are lots of threads here about how to handle that.

Sounds like it will be a fun commuter. Good luck and post some pics when you get going on it.