Very hard to make recommendations w/o knowing the spcs. Wgat cooler you buy very much depends on what CPU you have. Aside from getting the right hardware to match your socet, the ability yo overclock w/ an aftermarket cooler allows for perfpormance increases. If it's just games, then it might not be that much compared to applications where it can be very significant.
Your PC case has a CPU cooler height limitation 155mm .... As most folks don't use the stock cooler, a poll of your friends and family should come up with a few witha replacement laying in a draw .... alternately .... you could just take the fan off theirs and put on your,
saving you a fair amount of time and effort. Here's one for a buck amd a complete cooler for $2 ... make sure you get for correct socket.
<p dir="ltr">Intel Copper Base Stock Cooler Fan Heatsink for i7 E97378-001 - USED. Condition is Used. Fan is in excellent condition, aside from pins. Shipped with USPS Priority Mail.</p> <p dir="ltr">Note: The push pins are not in brand new factory condition (have some slack). You may need to...
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However, provided you have a CPU that makes it worthwhile, if you are going to invest the T & E in ordering, unboxing, taking old cooler off, cleaning the CPU, installing new CPU .... and considering the differences in performnce and noise ... a $35 Hyper 212 or a even an extra $15 or $20 is not that significant.
With a decent CPU, my 1st option would be the Scuthe Fuma usually goes for about $55.
a) Its cools your CPU 11C better than the Hyper 212
b) and it is 3 dbA quieter
In short .....
a) Your easiest and most cost effective option is a rep'acement fan costing you between nothing and a dollar.
b) Your best option from a performance and noise option would be a Fuma 2 ... if you had a CPU that would make a difference.
My guess is though, if the CPU could benefit, you'd have put it in the OP ... therefore Option a) I would think is your best bet