Ah yes ok, if you have a PHP/MYSQL backend then you wont need a full dedicated machine to run your own software on.
In that case the VPS solution that you have spotted should work out fine for you. They have taken a server and split into into smaller chunks and hand those out for sale separately which splits the cost among all those on the box.
This is the key thing you're looking for:
Management - New Web Control Panel, RESTful API , KVM, root access
This means you'll have full access to do anything you want (within reason) to your virtual machine, but they also have nice tools/control panels to make things a lot easier.
Payment with OVH are very flexible. You can pay as much (eg. 12 months) or as little (down to 1 month at a time) as you want.
They might even have a discount on place for that service that kicks in when you've been using it for over a year where the price goes down (not 100% sure on that with the VPS service).
They send you a reminder email when you are at certain intervals from your expiry with a link to continue payment, click and follow the details, nice and easy.
Check here for more information:
http://www.ovh.co.uk/support/termsofser ... t_proc.xml
And have fun
PS. I'm not sponsored by OVH, just a happy user.