The EBOOT.BIN and BOOT.BIN files located in /SYSDIR are required.
I haven't had any problems from removing the UPDATE folder (/SYSDIR/UPDATE) and it's contents but I can't say for sure it will work for all ISO's. I think generally keeping/removing it is just a matter of personal preference. The only advantage I can think of for keeping it is that you will have the updates if you ever need them and can't find them anywhere else for some strange reason.
The best advice I can give you is make a backup of your original ISO and experiment. You will need to make sure that you import the files into umdgen in the right order. You can do this easily by generating a file list from the original ISO with a utility such as IsoBuster and then import it into UMDGen after you have imported all the files for your new ISO. UMDGen will then make sure everything is in the correct order.
You can save more space (very little usually) by going to tools -> iso padding and then selecting no padding. I use UMD Standard to be on the safe side... the amount of space saved isn't worth it considering the time that it would take to recompile the ISO if it doesn't work.
If you want to play around with the padding let me know what your results are. ;-)
If you have trouble ripping a particular ISO, search google because there is probably a special method required for ripping that ISO.
And if you need a more detailed explanation just give me a shout!