You have asked "What is the best car I could buy? Also, should I build it myself or get one from the showroom?"
As many other posts here suggest, the first question is kind of meaningless without knowing what you want to do with said car. Is it for trips around town? To carry 7 kids? A lean mean street-fightin' machine?
As for the second question, if your budget is $50k, then I suggest neither. You cannot (should not try to) build a general-purpose HPC solution and its infrastructure for that kind of money. If your use-case is not heavily dependent on high-bandwidth data transfer then definitely consider AWS/Google compute/Azure. If you have a very specialized use-case, perhaps a single compute job that was trivially parallelizable with little or no I/O, you could probably put something together for $50k and run it under a desk. But general-purpose HPC is not just a bunch of server units. A high-speed switch between your compute nodes alone could cost that much. A very basic chassis from Dell suitable as a compute node costs around $5k. Stuff it full of memory, 2 or 4 xeons, GPUs if you need them, fast local scratch disk, redundant 10GB network connects... again, you're looking well north of $25k per unit. Not to mention, as others have, you need a climate-controlled room with abundant, reliable and redundant power to put the thing in.
All science is either physics or stamp collecting. -- Ernest Rutherford