You should be able to run up to 5 servers even on a 256MB VPS, so you're within budget for most providers. ShoutCast server is very lightweight, under 5 MB. Processing power is irrelevant as well, as it takes more to encode the stream than to serve it.
Your main issue will be bandwidth, as SC uses quite a bit. Even to continuously stream to 1 listener at 96kbps one day is something like 8 GB ((96kb * 86400) / 1024 = 8100mb). Thats around 250 GB per month.
Try to look for a pay-as-you go streaming provider, it might meet your requirements.
Also, heck out http://www.radiotoolbox.com/
, they have some bandwidth calculators.