DreamHost started to install ffmpeg last year on their servers, the path is /usr/bin/ffmpeg. Currently they offer 1 hosting plan, it includes 500 GB disk space and 5 TB of bandwidth.
Payment: Credit and debit cards, personal checks, money order, PayPal, Google checkout.
97 day money-back guarantee
When you sign up make sure you use one of the following DreamHost promo codes:
FFMPEG1 will give you 1 EXTRA free lifetime domain registration
FFMPEG50 will waive the setup fee for the monthly plan OR will give you $50 discount on the yearly plan.