I want to covert my 7 speed to 9. Currently I have a Shimano 600 derailleur. What parts do I need to make this work?
The community generally seems to advocate against upgrading your bike. I'm not sure why, it often makes alot more sense than buying new and more than buying used much of the time.
If your bike was originally equipped with Shimano 600 the likelyhood is that it's a good quality frame with other good components so it's probably worth upgrading if you love it.
If you wanty to upgrade to 9 speed, that's great. The transitions between gears are smoother and the jumps are smaller. You probably won't be able to extend the total range of gears by much though. current 9-speed shifters are Shimano Sora R3000 (or higher 3000-series) and route the gear and brake cables under the bar tape on drop bars so look alot neater. These are probably the most expensive purchase. You will also need a new rear wheel as yours will be one of the earlier 600 series groups if it was supplied as a 7-speed system from new. It is possible to replace the freehub body in some instances but this is not an easy route to go down.
You will also need a 9-speed cassette and chain. You will probably not be able to have a wider range than 11-28 on your 9-speed cassette with the existing 600 derailleur. All the other components will remain functional and are compatible.
Perhaps you should post some photos of your bike; you may gain more support.
Basically everything shifting related.
9 speed uses a narrower chain and a wider cassette so you’ll need: New shifters, new chain, new cassette, new rear derailleur, new chainrings. Your old front derailleur+shifter might work. New cables+cable housing will probably be necessary. It’s possible you need a new rear hub (could be cheaper to get a whole wheel) if your old hub uses a freewheel-style cassette instead of freehub.
Upgrading to 8 speed would be simpler, I think you’d only need a new shifter and new cassette (and possibly new rear hub).