I moved to AWS a few months ago purely for the convenience of being able scale it up as my needs grow.
I started with t2.micro , 1gb RAM and 30GB HD Windows Server 2008 with 1 Elastic IP and moved my domain into it. Installed MySQL in Oregon....
Have since changed it a bit... moved to t2.small 2gb RAM , 100 GB HD, moved MySQL to RDS and then moved the entire lot to Frankfurt to accommodate the EU data retention laws.
My app will be fine as it is for a while but I will scale up again when I need to.
I knew nothing about AWS when I started (still don't know much) but decided to jump into the deep end of the pool and try it out. I have thoroughly enjoyed the experience and learnt a hell of a lot along the way.
Trying to work out what it is going to cost I found almost impossible but it becomes a lot clearer once you give it a go..... Of course if you dont like it you can always turn it off.
Here is my current daily cost....

I will say that it can all be very confusing but there is lots of docs around (albeit they are updated regularly but there is a fair bit of outdated info around) and wading through it is worth the effort. I can keep track of everything on my phone including the cost and it has been 100% reliable.