The 4590 is a locked core cpu so you won't be overclocking it. If you live in a hot climate and have the cpu under load a lot or want a quieter cooler, I'd go for something like a 212 evo, 212 plus or be quiet pure rock. I wouldn't expect a lot out of a $10 cooler. If you'll notice, it's similar to the stock cooler. A large hunk of metal with a small fan on it. More efficient coolers use heat pipes with cooling fins and tend to be pretty quiet (like the ones I mentioned). If considering the alpine 11 plus, I'd save the $10 and use the stock cooler.
It should run fine on the stock cooler, even if it gets a bit warm. The only real reason for an aftermarket cooler on a locked cpu is to get a quieter cooler. The stock cooler can be a bit noisy if it has to spin up to full speed often. I'm also not a fan of the junky plastic clips on the stock cooler, most aftermarket coolers use a backplate with screws to hold everything in place. Less chance for it to work its way loose and lose good contact with the cpu like the stock coolers are prone to.
Liquid cooling is safe enough most of the time, leaks can happen. More than likely other things will be problematic like the software, fan control, pumps going bad etc. They use pretty cheapy parts on aio coolers but it's to keep cost down. An aio vs a custom loop buying quality individual parts is $60-100 vs $250-300+ so it stands to reason. There's no reason to need water cooling for a locked cpu. Small budget aio's don't cool much better than decent air coolers, tend to be louder etc. Most larger air coolers outperform the budget aio's and come close to the larger aio's like the h100i while costing less and less moving parts to break. Either aio or large air cooler (aka noctua nh-d14, phanteks tc14pe or similar) are way overkill for a 4590 and a waste of money.
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