Below is a list of cloud hosting services that we highly recommend. We frequently use them with our clients and have never had any issues with them. They all have a 99.9% Uptime Guarantee and provide full access to the cloud machines at the root level.
Keep in mind, both of these will require a Server Admin to maintain and manage the account as well as any servers that are created within the account. Modded can handle that for you under a maintenance plan if you do not have someone already on staff.