I'm kind of wondering how you can call a service that costs almost $83 per month at minimum "not even that expensive", when dedicated Minecraft server hosting companies like Creeperhost sell you a completely sufficient server slot for £9 a month.
You don't need an m1.medium to run a single player server. You can do it with a micro unless you start using world anchors, which ranges from $0-$15 depending on if you're still eligable for Free Tier service. That is why it can be cheap. If you are using a more complex world with >20 world anchors, I agree low-tier EC2 is not a good call.
M1.mediums are only for multiplayer servers. I rotunely have many players and multiple world anchors on my server, so yeah I pay a lot more. I can also host multiple servers there (so long as they don't BOTH fill up). My experience is this server is better in every way to the ones Minefold sold me on the cheap, and Amazon makes it very easy to spin down the instances and then spin them back up at need. For example, are you going on vacation? Turn that sucker off.
Amazon EC2 is extremely cost efficient when you're booting up the instance on demand for an hour or three a day or so. As a 24/7 thing, like Stormseeker would need, it's utterly uncompetitive.
I think the real draw of EC2 is that you can manage the server and they make pretty realistic performance promises. Lots of people give you utterly oversold virtualized instances that cause multiple server crashes, or have so heavily modified the minecraft server engine for virtualized environments (e.g., Minefold) that you can't do what you want to do.
But if you're in the UK, then I don't know what's cheapest for you. I just know that $83/mo for a box I am using for multiple things besides just minecraft is just fine, given that my server has seen >15 players at once and not had any significant problems, whereas most of the hosted services I've tried weep at >6 people.