its complicated because there exists .NET 4 and .NET 4.5, you need 4.5 but in one sense 4.5 is still considered 4.0 runtime, so it is not clear what you will get
also once you move your current site to 4.5 hosting it will immediately be broken because there are things in the web.config file for 3.5 which are not compatible, explained in the 10th item on our faq
I'm not going to be able to help you step by step, I highly encourage you to get help from someone experienced, I'm not available myself and the only ones I know that I can recommend with confidence to be able to solve each problem as it comes up in your upgrade is the i7media guys