Air coolers the regular Standby's like the Hyper 212 are probably still good, just have to order the mounting bracket for some of them.
As far as entry level Liquid cooling.
Cooler Master MasterLiquid 120(non-pro version), comes AM4 Compatible out of the box, and works very well. Stock Push/Pull dual fan layout with 120mm type Radiator and decent tube length.
https://www.newegg.com/Product/Product.aspx?item=N82E16835103233
For me the MSI Core Frozr L Processor Cooler. Made for AM4
I build it on a 1600X
Open Box: MSI Core Frozr L 120mm Hydro-Dynamic Bearing CPU Cooling - Newegg.com