Before even installing the operating system, spend some time with the below:
Run MemTest. I think two passes is enough, but others may comment here on that further. (It is going to take a few hours)
If you don't know what MemTest is, what "passes" are, etc., no problem. Prepare now, by going to :
http://www.memtest86.com . Read. Download. (It is free).
Create a bootable CD.
I have experienced purchasing brand new ram, and having a bad stick. While it is depressing to discover, it is better to discover it at this stage, rather than later after having installed OS, and wondering why strange things happen.
Google the manufacturer of your hard drive.
Visit their website, and download their free diagnostic software. Create a bootable CD.
Test your hard drive with it.
If there is a 'long' test and a 'short' test, I seem to remember that the short test is enough, but hopefully someone else will comment.
After installing OS, you may want to test further with a stress test.
Google for free stress test software. It has been a while for me, but some names that come to mind are:
OCCT, Linpack, and Prime95. Others here may comment on which is 'best', or perhaps even name others.
Again, prepare now by visiting their sites. Read. Download, etc.
I don't remember how long to let one of these run, for a good test. Hopefully someone else will comment.