I've done some browsing around looking for various hosts and came across creeperhost.net
They have a package with 1024MB RAM, 30GB disk space, and unlimited bandwidth for ~$15/month. From what I've seen they are both reliable and go above and beyond with customer service. They also give you the ability to install various mods yourself with some minimal support to quickly add some of them.
A bit later in the month I'd be willing to try them out for a month to see how we like it and how well it works for our needs. As for mods I'd probably install RedPower (it adds a few new things to mine, new blocks, some machines, and improves upon redstone.), chop tree to let me chop down trees in one fell swoop, RailCraft for improved rail things, and Industrial Craft.
To see how well this works I'm going to try and set up a MP server on a computer at home to see how well it works out.