I know of a few and when I wanted one I chose Digital Ocean. I used to use it for building android from source but now just some web site testing. You will have to install the desktop and remote package yourself though on some distros.https://www.digitalocean.com/?refcode=7e1f82f7cb31
You can't beat the cost either. $10-$20 a month for a decent box and all of their systems run SSDs. These machines will have full external IP Addresses so I recommend a firewall. They are more setup to be servers but they do not have an issue with users installing the desktop environments. If you needed help I could walk you through installing the desktop environment and then enabling remote access. There are some great tutorials right on the site as well for doing this that even include making the firewall changes to only allow remote access from your computer and a few other things.
The pricing for backups is 20% of the cost of the virtual server. So if you want to enable backups for a $5/mo virtual server, the cost for backups will be $1/mo.
The price for snapshots will be $0.02 per GB of snapshot storage per month.
You can start with the $5 a month one and resize to a larger droplet if needed. I believe you can also go down in droplet size.
"Please note that once you resize to a larger disk, you will no longer be able to select a smaller plan for a fast-resize. This is because there will be a disk mismatch and we do not currently support shrinking a virtual server's disk." But you can shrink the CPU and RAM if you give it too much.
Snap shots are very cheap and allow you to get a little crazy with changes since you can easily restore the system in a matter of minutes. You can also create new machines from a snapshot and run things side by side. You are only every charged for what you use and destroy droplets at any time.
Hope this helps and if you do give them a look please use the link provided as you will get $10 in account credits. *I get $25 once you get to $25 in total billing. This is basically a free two month trial for you on their smallest size droplet.