Installing Mountain Lion on MacBook Pro with new HDD

I just had the hard drive replaced on my 2010 MacBook Pro. I was able to backup all my data before the repair, but I was still running Snow Leopard (OS X 10.6.8, I think) and I have been meaning to upgrade to Mountain Lion. Would it be best for me to install the new OS before transfering my backed up data? And if so, how can I go about doing that?

Thanks.

You will need to install Snow Leopard OS X.6.8 to be able to access the App Store to purchase Mountain Lion for $20.00. You should have the Snow Leopard disc as that is what your MBP came with.

I guess I'm asking if it's best to restore the old Time Machine backup before or after installing the new OS.

Install the OS and then with with external drive containing Time Machine connected, go into utilities and use Migration Assistant. When it is restored to OS X.6.8 then go into the App Store for Mountain lion. As a suggestion burn a copy to a USB flash drive, 8GB, before running the Installer. Here is how:-

http://liondiskmaker.com