You'd be able to meet these requirements on a GoDaddy VPS or dedicated server, but certain things like FFMPEG and that super long PHP timeout aren't going to work on shared. Being on a VPS will mean you're on your own figuring out configuration though.
Based on those requirements looking like you'd be uploading and transcoding video with php, you're only going to get reasonable performance from a dedicated server, and even then the
memory_limit (with 1MB more then the maximum video upload size)
requirement is interesting, the most RAM you can get is 32gb.