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How to find web hosting that meets my requirements?

In case you want to skip to the crux of my inquiry just read the bold type.

I just finished my CS degree (at 39 years old :-)). For my final project I designed and built a system that can provide local positioning / location awareness to mobile wifi devices (only have Android client thus far). The server receives data from clients, processes it, and responds to the clients with a messages containing information about their respective locations. I would like to continue the project (perhaps release as open source but that is a different discussion). Thus far my server application has been running on the CS department's hardware where I could pretty much do whatever I wanted. I'm getting kicked off that system in a few weeks so I have to find a new home for my server application.

I need a host that will let me run my Java server (along w/ mySQL db) -- preferably on the cheap since I haven't yet got a job. I have very little experience with the "real world" of web development / hosting. I'm having trouble figuring out what kind of hosting service will let me run my application as is. If that turns out to be a tall order then I need to know what my options are for changing thing so that I can get up and running with some hosting.

As an aside, I'm also researching whether or not I should rewrite this in a different language. Trying to figure out if there is a substantially better (for whatever reason) one for what I'm doing. This might also potentially have a bearing on my hosting needs. One possibility is to write the server in something more widely accepted by hosting services.

I have been searching for answers to my question and haven't found quite what I'm looking for. Part of the problem might be that I don't know exactly what terminology to use. If there is a good answer to this question elsewhere please feel free to point me towards it.

Thanks for help / advice.