EC2 is like co-location in a cloud, so you will need to handle all sysadmin tasks yourself (however, you can select an image that already has LAMP installed). A single small EC2 instance is around $75 per month + bandwidth.
You can also go with a platform on top of EC2, like RightScale, which gives you some support, including MySQL, but it's expensive ($500 per month!). I don't have experience with other services but I do use the RightScale dashboard for creating/restarting/terminating instances.
There are many advantages to going with EC2 though, if you can absorb the admin work. For example, if you need to do some heavy crunching you can run another instance only for the time of the crunching, say 12 hours, and that's all you pay for (12 * $0.80, if you were to use an extra large instance).