I'm interested in setting up my own website-based game (PBBG) as a hobby. Traffic shouldn't be too much, a couple of dozen users at a time on average.
From all the reviews I've seen, Ruby on Rails is the best way to go as far as coding and platform. As far as OS goes, I've only used Ubuntu in the past and, while it worked smoothly, I didn't feel very comfortable in it.
Is there a recommended version of Linux for a RonR app?
If you dont have much experience with any Linux distrobution, I would just pick a popular one because it will provide tons of community support. I personally would recommend Fedora or Ubuntu. You will then be able to find tons of How-Tos for just about any tasks you want to accomplish.
edit: Here is a nice resource about different linux distrobutions: http://distrowatch.com/
As far as I can tell there is no recommended version of Linux for deploying Ruby on Rails applications. You can basically use any Linux/BSD distribution that you feel comfortable with.
Have you tried Arch Linux? I use it on 90% of the production servers and I didn't had any problems so far. It's lightweight, flexible and simple. Also updating and installing new packages is a very straight forward process.
You should also take a look at Django.
Django is a high-level Python Web framework that encourages rapid development and clean, pragmatic design.
To add to my comment to @Jason's answer. I know you said you were uncomfortable in Ubuntu, but if you're moving over to Linux then you're going to be uncomfortable for a while. With all the community help out there, you'll be in good hands.
p.s I always google: ubuntu whateverImLookingFor
Do you have to host it yourself? Not knowing your environment, but if you're on a home connection you'll have to setup dynamic DNS and your upload bandwidth is probably throttled (I don't know how much game data you'll be serving for the players per session) and could be a bottleneck.
I know I wouldn't want to run and manage my own Web server if I was not comfortable with it. Better off getting an inexpensive hosting account (~$10/month) and let them handle uptime, backup, DNS, security, etc. while you focus on making your game.
There's a pile of recommended RoR hosting providers on the RoR Website.