Pioneer is the best workhorse for the duty you are talking about.

https://www.amazon.com/Pioneer-Pro-DJ-Black-PLX-500-K/dp/B01K1WUS9O

and another version touching your price limit from another side

https://www.amazon.com/Pioneer-DJ-Direct-Turntable-PLX-1000/dp/B00O8U3ZI2/ref=sr_1_2?crid=1OEGQXEWRAOYO&keywords=pioneer+dj+plx-1000&qid=1685609463&sprefix=pioneer+plx-1000%2Caps%2C205&sr=8-2