Ram, rails is ram bound not cpu bound in 95% of the cases I see.
More RAM, definately. And because it's a dedicated server, as long as you're
not running any other CPU intensive processes at the same time the Celeron D
should be enough... although if you can opt for a Pentium rather than a
Celeron you may find the additional cache helps.
You've not specified which OS your server will be based on. I would assume
the timeshare server is based on *nix. If the dedicated server is also *nix
then 1GB should be sufficient, however if it will run Windows then you may
find you need to add more memory.