[W]hat type of specific manual cleaning (insert brand name here) tools should I use if I just want to clean & play?
Brushro, to just play your records, a carbon fiber anti-static brush as suggested by Jmcgrogan2 and Dan_ed above, works great. It will clear the surface dust, it just won't clean the record of accumulated gunk that may be down in the grooves. For cleaning the record, you can't avoid some sort of wet cleaning process. But wet cleaning can be done without a machine. Some report good results just cleaning at the sink with a liquid detergent and water solution (not soap!). I've had good experience manually cleaning with Disc Doctor following the
Disc Doctor Miracle Record Cleaner manual cleaning procedure -- a towel to set the LP on, the DD cleaning brushes (this is what does the cleaning), some cotton cloths to dry off, and a rack to set the records in to dry. For me, this is probably the simplest true cleaning process that doesn't involve the expense of a machine.
Congratulations on getting back into vinyl!
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