We have been successful with buying and using our own dedicated hardware - for example one can get a 512GB RAM, 24 core, 100TB server for $25K or so. That can handle a surprising amount of work and it is a lot simpler to run and manage than a cluster. It is basically just one simple linux server and we are parallelizing via GNU Parallel. You should run some tests to see if that works for your needs.
Now the next step that I would recommend would not be to to building your own cluster - that in turn has massive costs in managing and maintaining it. Unless you already have the staff for it, though I doubt it, I imagine hospitals running windows. At that point, having staff supporting both linux and Windows based systems and integrate a diverse infrastructure gets very expensive. In that case I recommend to go with a service such as DNA Nexus where you don't need to bear the costs of running an infrastructure.
(Edit: corrected prices, specs)
Some of this has been already discussed here: http://seqanswers.com/forums/showthread.php?t=64332
I don't think that a three year old thread is relevant especially when it comes to bioinformatics and IT
The thread I linked above was started by cmccabe on 17th November 2015. Not sure where you are seeing a three year old thread.
sorry my bad, I misread the date
I do NGS on S. pombe which has 12.6 mbp genome. I started doing on a workstation because I thought it would be more convenient but later I learned to do cluster computing and oh that is way better than having my own VM, workstation etc.
Consider you are working with human genome and I guess you are planning big projects for your hospital, so definitely cluster computer.