The 5.03 Gen-C and 6.20 TN-C and 6.35 PRO are the different hacks, and like I said you want a 5.03 hack, which will be 5.03 Gen-C (with prome-4 addon). This covered by like the second question in the FAQ.
You find what module your PSP is by running a HEN for the current firmware version (6.20 or 6.35) and then running the module checker. That tells you if it's a 03g or a 04g or whatever, but you can also tell that by the firmware that ORIGINALLY came on the PSP (which you want to be 5.03 or less).
You can downgrade to 5.03 from 6.20 or 6.35 assuming that the PSP is a 03g and came with 5.03 or less installed in the first place.
Gen-C is better, just sometimes we have to use older install methods that install older custom firmwares because the newer ones use different install methods, so you downgrade to an older one and then update to a newer one.