$150 per year would work out as $12.50 a month which would be hard to find a reliable managed VPS for. A unmanaged VPS and maybe request on install have the company install FFMpeg (if they are nice enough). Then you might be able to get a VPS for that amount.
Another question, what sort of spec are you after? As FFMpeg can use a good amount of memory and sometimes hit the CPU load.
@naruto7 unmanaged VPS's are normally without any control panel (or free version) and if there is a problem on the VPS non-hardware then you are required to fix it.. Or if you wish to install software you will need to do this yourself. Some companies will help with software installs from the start, but you will need to ask
If you have to ask, go managed. Any fully managed vps/dedicated hosting provider should be able to install FFmpeg for you for FREE. Be careful though as some providers clamming they're fully managed will still try and charge you admin time to install FFmpeg.
If you choose an unmanaged VPS you will have to pay admin time of around $75 just for them to install FFmpeg.