Do you have any problems with learning the command line? How much do you currently spend for shared hosting? You can get a Digital Ocean VPS for about $10 per month that should be suitable for a few thousand members (may need to upgrade depending on how many of them are active concurrently), but it'd require setting up things yourself. I have a DO droplet that supports multiple websites with thousands of members across them (so far no Oxwall installation is live though) without any problems.
They have plenty of tutorials and help forums on how to set things up. For certain people, like myself, it's very fun maintaining your own VPS and server packages. The versatility over shared hosting is great without having to break the bank.