I would upgrade to a VPS - they are relatively cheap, with some starting at the price of a reseller hosting package. If you aren't that experienced with Linux (if you choose a Linux VPS), then I would advise that you go with a semi-managed or fully managed solution until you are able to go it alone. It's a bit of a learning curve, but it is worthwhile.
The amount of RAM and everything depends on if you wish to run a certain control panel (e.g. cPanel), and your resource usage. If you do want cPanel, expect a price increase in some cases.
There are plenty of web hosts offering high quality VPS solutions out there, and if you go and speak to them, I am sure that they would be more than happy to answer any questions that you may have.