Digital Ocean is fine though you will hear arguments about Linode providing more cpu power for the dollar.
If you build a VPS with DO, you are your own security. If you do not have the skill the setup and manage a linux server in it's rawest form then you are in for a world of hurt.
If you know how to manage a linux server, a community that small will easily get by on the $5 a month plan IF the server is configured properly. An improper config on a minimal server is going to leave the thing starving while a good config could handle 250 users / 1000 requests per second. I would recommend something better if you can afford it. 2GB of ram and a couple of dedicated cpu cores will perform for a small forum.
I doubt you are ready for this but my first piece of advice for DO is to enable swap.
If you uploaded an old database and the latest copy or a newer version of xenforo you should only need to run the install to update everything. Off the top of my head I forget but it should be like www.yourdomain.com/install/index.php or maybe its install/install.php