I am just getting started in fixing bikes, and seem to have the most difficulty in figuring out what is compatible with what.

For example, I have an older (not exactly sure how old) Scattante 670 with a newer, but still old, 9-speed Ultegra groupset. I was looking to replace the RD, but I have no idea what I could replace it with. I assume I don't need to find the exact same derailleur, but would most 9-speed RDs work, or do I need to stick with Shimano parts to match other parts for some reason? Also, I was looking to get shorter cranks, but wasn't sure how to match the crankset with the bottom bracket. Do I need to disassemble it all and use calipers to measure everything since there are very few markings of size and measurement on most parts?

Any tips on finding compatible parts rather than buying parts and realizign they're wrong would be great.