What you have now is likely going to be just fine. That’s not an overclockable chip. Who told you it wouldn’t be?

If you're not going to overclock and dump more Vcore on the thing, don't waste money on a larger/more expensive cooler that's made to keep overclocked processors cool..Your H60 should do more than just fine.
 
4900MHZ, or 4.9GHz is the i7-9700K stock Max Turbo speed out of the box.
 
Whoever advised you, advised you wrong.
 
You can, if you want to, overclock it by raising the CPU Multiplier (A 'K' suffix means it has an unlocked multiplier) and CPU Core Voltage (Vcore) as needed in the BIOS for an overclock, but raising the Vcore will raise the temperature.
 
Just use some decent Thermal Paste such as MX-4..And don't put too much..Too much is as bad as too little..A BB-sized drop in the middle of the CPU will be good..Tighten down the cooler block incrementally in a diagonal pattern.

Sorry, again I misspoke. I am considering the DG-86. Its a behemoth, but for the price, it looks like it has a ton of customizable options. I just had another guy in a gaming group tell me that I would need a triple radiator. But then I read a Toms Hardware review that said that it ran fine on air cooling. I wish there was consistency in the PC world