Yeah, you'll definitely want a better one if you wish to take it further. Cryorig H7 is my personal favorite because it's a nice quiet good performing cooler for $30. Not the greatest but darn fine. Case needs a decent gap between the motherboard and size to fit it though (~150mm)
Noctua D14, U12S, U14S, etc. are also quite good fan coolers. There's a large army of good ones.
I don't recommend water cooling personally, expensive and more stuff that could break.