Back of the envelope calculation -

A passenger instance for a typical small app takes 30-40 MB. You will be able to run 4-5 passenger instances on a small 512 MB slice.

Assuming that the slowest request in your app takes 100 ms, one passenger instance can handle 10 requests/sec. 5 instances can handle 50 requests/sec.

Tweak the numbers according to your app and get a rough idea of the hardware requirements.

A 512 MB VPS on Linode costs 20 dollars.