Try something cheap and easy to see what the possibilities are before investing in an expensive machine, which will vacuum records dry (good), but will scrub them wet no better (or worse) than you can do by hand.
You do need to get a fine-nap velvet record brush to clean down into the grooves, but the heck with designer cleaning fluids, you can make an inexpensive mold-combating fluid with ingredients you probably already have around the house or can pick up at any discount/drug store. Combine a 1/2 cup of clear 70/30 (isopropyl/water) rubbing alcohol (not "denatured" or containing lanolin, etc.) with several drops of a dye-and-perfume "free" laundry detergent formulated with enzymes (such as Tide Free) and several drops of standard chlorine bleach.
Prepare a flat working surface on a kitchen countertop, using either a towel or something if you must, but a better bet is a rubber turntable mat that you can easily rinse and dry periodically during a cleaning session, and won't recontaminate the turned-down side of a record with lint or absorbed dirty fluid. Thoroughly wet the the playing surface of the record (none of this 2-3 drops of fluid business, you need to be able to float whatever contaminents are released) by spreading out a bead of fluid with the brush and then scrub concentrically with the grooves for a solid minute, working your way back and forth around the whole record side, putting a little elbow grease into it. Rinse with filtered water if available (either under a filtered tap if you have it, keeping the record angled down from the label while rotating through the stream, or in a large bowl filled to just below the label of a vertically-dipped record, rotating the record through the water), and dry gently with premium paper towels (such as Bounty, which won't shed fibers) again going concentrically with the grooves.
You may have to repeat the process if the contamination is bad, and if two or three cleanings don't change the appearance any further, play-test it anyway -- the permanent damage might be mostly cosmetic. You'll also need some kind of bristle brush to help clean your velvet brush under rinse water between passes -- a new toothbrush will suffice. If you decide to clean a lot of the records by hand (even if you eventually get a vacuum machine for final cleaning and/or drying) and want a better working surface, and happen to live near an Ikea store, try this.
Best of luck!