I really like Corsair parts, they're probably the top line right now for auxiliary parts. Doesn't hurt I get a discount from them usually via vendor connections.
However, 60mm is kinda out-dated so you actually typically don't have a whole lot of choices. Just make sure you find one that fits your socket. Typically it is better to shop for CPU coolers via CPU socket, as a lot of modern ones can extend the fan out separate via internal watercooling pumps.
For example, we'll use my current cooler:
https://www.amazon.com/Corsair-CW-9060025-WW-Radiator-Advanced-Lighting/dp/B019EXSSBG/ref=sr_1_7?s=pc&ie=UTF8&qid=1520277517&sr=1-7&keywords=cpu+cooler
As part of the specs, it lists the sockets: Modular, tool-free mounting bracket for installation on Intel LGA 1150, 1151, 1155, 1156, 1366, 2011, 2011-3 and most modern CPUs. (I have Intel) The smaller portion is the part that applies to the actual CPU. The fans attach to the outside of the case. Liquid is regulated internally so I don't have to do any fidgeting with liquid myself. So basically, although right over the cpu itself can't fit a large fan, I can still get decent cooling space. Of course, if your machine is super old to have a 60mm cpu cooler, then it might be a tight case anyways.
Other option that highlights the same idea: https://www.amazon.com/Corsair-CW-9060007-WW-Performance-Liquid-Cooler/dp/B00A0HZMGA/ref=sr_1_5?s=pc&ie=UTF8&qid=1520277517&sr=1-5&keywords=cpu+cooler
If you really need the 60mm size: https://www.amazon.com/Profile-Aluminum-Structure-Connector-Internal/dp/B079RMM25W/ref=sr_1_6?s=electronics&ie=UTF8&qid=1520278055&sr=1-6&keywords=60mm+cpu+cooler
Thermal Compound if you need it (a lot of them don't come with it) https://www.amazon.com/ARCTIC-ORACO-MX40001-BL-Compound-Performance-Interface/dp/B0045JCFLY/ref=sr_1_13?s=pc&ie=UTF8&qid=1520277517&sr=1-13&keywords=cpu%2Bcooler&th=1
One tube of it lasts ages.
Kirkendall 1st MRB's post in Pending Reply- PC Restarting or turning off unexpectedly was marked as the answer