If you're just learning, the SQL Database on Azure will do a lot of what you need. They have free accounts you can set up. Also, check out Amazon Web Services. You can set up a free database account there too (as long as you keep the size nice and small). There are probably others out there.
"The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood"
- Theodore Roosevelt
Author of:
SQL Server Execution Plans
SQL Server Query Performance Tuning