Moving to a new VPS; what to look for

I've actually been managing a website for several years, but don't have much experience in moving to a new VPS.

To cut a long story short, we've spent too long getting our new CMS/webstore ready and have delayed upgrading until that was done, but the current Windows 2003 setup is 6-8 years old(!) and now very low spec and poor value- and the once-great host we were with is no longer what it was.

We get around 6000 ".htm/.html" page hits a day, and obviously multiples of that when included files are, er... included, but would like to improve this (so need headroom). We've also a number of other sites with much lower traffic.

Questions...

- Is it worth trying to get Windows Server 2012, since it's had time to mature now? Some places still only seem to offer 2008, and 2012 has the maligned Metro interface.
- I'm assuming we should probably be ditching Server 2003 (the age of the version of IIS on it was a nuisance in itself). Is that right?
- How many cores should we go for?
- How much RAM?

We'd like some overhead and room for growth, but there's no point in wasting money.

We also need to be able to have the host up and running at the same time as the old site so we can install it, test it and get it working. The DNS would still point at the old site, but I could change my hosts file to point to the new one for testing.

(When we were moving another company's website to our current host, they told us they couldn't set it up until the DNS was pointing towards the new web space! I thought this was a bit poor, and read other people elsewhere confirming my suspicions that this should have been not just doable, but expected).

Our virtual machine reports we're currently running an "AMD Opteron 270 Dual Core 1.99GHz" (circa 2005) with 512MB RAM. Wonder if that's hurting our performance?

Any feedback would be much appreciated. Thanks!

- Smichy