Good suggestion to go right from your record cleaning machine into a new rice paper sleeve.
I think you should seriously consider using Magic Eraser to clean your stylus instead of the gel goop. There are many reasons why.
1)dirt gets transferred to the gel, so over time you are dipping into a dirtier "cleaner".
2)Depending on shape of your cantilever, gel can get deposited there and buildup.
3)Magic Eraser safely cleans your stylus much more effectively, and you can see & hear the difference(plus it is so cheap, it's almost free).
I switched from the gel goop to Magic Eraser a few years ago, and couldn't be happier w/it. Same results for many hear. Search the archives for details.
One other thing I use that's kinda neat is the AcousTech giant-sized carbon fibre brush(w/grounding wire). It quickly allows me to remove the stray dog hair, etc. from LP with one swipe. I do this last after using a Walker Talisman. Cheers,
Spencer