If you are new to Rails, configurations and even Linux, the best option would be Apache / Nginx + Phusion Passenger + REE . If your VPS is something you control, such as Slicehost, Webbynode, Linode or the like, then this will be an easier route.
Slicehost articles should help you a lot by going through each step of setting up your VPS. And the steps even work on other VPS hosting companies, just match the Linux distribution.
If you are really green for RoR and configured VPSes's-es (?), And if you do not need more than 512 MB of fragment - I agree with Chuck, start with Heroku until you hit about 3-4 dinosaurs. And since the Redmine demo is on Heroku - you know that it works!
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