Give me some specs for a cheap >$750 minecraft server build?

The computer is strictly for a public server, the case size is micro atx, and if possible to save on costs run off of 300W. Also please don't link a website that has a guide or anything my parental controls glitched and blocks off certain computer related websites. Also it didn't need to be any mega powerhouse, just enough to keep a server running 24/7 and also do I do air or liquid cooling.

Go for i5 but i agree i3 would do decent thing

You just need a computer with a decent amount of memory and a good processor. Any cheap graphics card or even integrated graphics will do because the server doesn't display any graphics. This should be achievable for well under your budget. Air cooling should be fine unless you're planning to overclock it by a ridiculous amount, but it's cheaper to buy a faster processor and air cool it than buy a slower one, overclock it and add expensive liquid cooling to it. A Core i5 is a good choice, the server isn't multithreaded so it doesn't benefit from the hyperthreading of an i7 or lots of processor cores, this also means that a decent dual core i3 might do the job just as well.