VPS is going to be your cheapest option, but you'll need to be mindful of a host's policy regarding CPU usage. If your application doesn't use much in the way of RAM or CPU, then you'll probably be fine. I have applications that I run 24/7 on my Windows laptop that use the CPU 100% the entire time. They're a similar concept to [email protected] and the like. Most hosts wouldn't want that on their server.