What's the best way to clean vinyl records?

If you want to do it cheap , then you have to do it yourself including some DIY construction .
There is a video on you tube that explains this method better than I probably will .
For @$60 purchase a small wet/dry shop vac , a plastic tailpiece for a sink and an old fashion drain stopper .
Cut a slit @ 6 in. long in the drain pipe and put the stopper in the big end of the pipe . Stick the other end of the pipe into the vac end piece on the end of the hose . Wrap a piece of micro fiber around the tube and cut a slit in it the same size as the one in the pipe . You have now made a record vacuum cleaning machine !
Now go to another store and get 2 of the old fashion ketchup squeeze bottles with caps on the spout , a bottle of 91% rubbing alcohol , a gallon of distilled water , 2
paint pad edger devices and a small bottle of dish soap .
Fill one of the ketchup bottles with distilled water and label it RINSE . In the other bottle just cover the bottom with dish soap , then fill up to @ 1in. from the top with distilled water and the last inch with the alcohol and shake it up . You have now made your cleaning and rinse solutions !
Set a record on a clean lint free towel and squirt some cleaning solution on it and spread it around with one of the paint pads . Let it sit for a bit and then use the pad again , in the direction of the grooves . Now vacuum off the dirty solution . Squirt some of the rinse solution onto the record and repeat the brushing with the second paint pad and vacuum dry . Now put a clean lint free towel onto the first one , under the record , and turn the record over to clean the other side . When done stand the record up to make sure that it is completely dry before returning it to the clean sleeve .
I used this method on side A (usually the heavier use side)
after cleaning the entire record in a Spin Clean tank using
their cleaning solution and drying towels . Both my wife and myself could tell a noticeable difference between the two sides of the record ! The DIY cleaned side had a little more detail , less background noise and more you-are-there presence .
For @ 70-75 dollars and a bit of extra work the DIY method did quite a bit better job than the @100 dollar Spin Clean method . This DIY method is now my preferred way .

Good luck .

This may be way over your idea for a cleaner but you asked for it.

The best version I have is the KL Audio LDP200 ultrasonic cleaner
Not cheap at $4,000 but it gives incredible results that really get out the unwanted material in the groove leading to better detail, low level resolution and quieter surfaces. Just lower the disc down into the machine and go about your business

I have a Loricraft cleaner as well and used the 4 stelp Walker process. It is very effective, especially for soiled records

The KL does a better job and doesn't require tons of your time
Change the distilled water every month and clean away

There is a similar ultrasonic cleaner the Audio Deck. Ut requires cleaning solutions and swapping out cleaning brushes but gives similar results.

This is like a major cartridge upgrade and even brings great improvement to new vinyl

i have used virtually all of the DIY options including steaming, strong cleaners, vacuums, and Ultrasonic. I really like the results using the scrubbing with a good brush (i like the mofi brush but have used several types) and using a steamer to heat the liquid before scrubbing. I vac after scrubbing and after two RO water rinse with great success. I have also built a Ultrasonic that IMO with the right cleaning solution is the best i have ever used. I built the vac cleaner and ultrasonic using techniques described on Diyaudio and here. For the really dirty records i pick up, i will do both cleaning with the scrubbing/rinse followed up by a Ultrasonic cleaning and final rinse with RO water. To many people cheap out on the rinse water and leave deposits on the records. I have over 4000 now and other than surface noise on some, they are remarkably quiet. I have my own cleaning solutions that i like but many commercial cleaners do an exceptional job. Good luck

I know Saki's method works very well and has modest cost. I suggest distilled water, max 5% isopropyl alcohol, dash of Dawn dishwashing soap (has alcohol as an ingredient). Rinse, rinse, rinse. Then I have used the "LAST" products (which I think are great) to finish off. Records are tougher than most think. When I've bought 'dirty' collections I've used soft brushes, gently, for washing and rinse. I've probably been more brutal than anyone would suggest-but it has salvaged records I would never have played - lest they rip out the needle.

Jump on a VPI 17F now..