any other supplies that are recommended?
I think a cheap brush set (I use these) should be all you need. If you are concerned about your suitcase player tracking heavy and "damaging" your albums then buying a vtf scale is cheap insurance to ensure its within range for your cartridge.
A lens cloth cant work, get a decent brush, something like https://www.amazon.com/AudioQuest-Anti-Static-record-cleaner-brush/dp/B0006VMBHI
EDIT: or this https://www.amazon.com/Boundless-Audio-Record-Cleaning-Kit/dp/B09G94FN98
Your local record shop should have a raft of options.... ask them. Also review Sharkamino's excellent cleaning guide https://www.reddit.com/user/sharkamino/comments/jpac5p/diy_wet_soak_vinyl_cleaning/
Boundless brushes - been using these 3 years with no problems.