Look at the excellent Pioneer PLX1000. Add a Nagaoka MP-110 cartridge. And as the records sound like they need a good cleaning, a Spin Clean.
I know it's a little over budget but you'll get a sturdy machine and you can upgrade the cables if desired. You might even start collecting a few more old records from stores.
https://www.amazon.com/Pioneer-DJ-Direct-Turntable-PLX-1000/dp/B00O8U3ZI2/
On the other hand, if it really is to just hear the ones you have a few times, and be done with it, the inexpensive Audio Technica LP-120 with a cleaning machine bundle for low money may be all you need.
https://www.amazon.com/Audio-Technica-AT-LP120XUSB-Direct-Drive-Turntable-Cleaner/dp/B07RDYH9S7/