With a 3-year reserved instance, using the "intensive usage" pricing (since it's always on), and in the cheapest availability zone. I get a price of 6.42$/month. I guess in practice, even for an personal thing, around 10GB of storage would be required (1$) (does the installed OS counts towards this number ?). Add 10GB of transfered data (1$), as a vpn/screen server is unlikely to have huge amounts of incoming data.
The final price is 8.42$. Which, for a 600MB ram server, is quite competitive. If I didn't forget something.
This is about the only use case where I would recommend AWS, though. Starting at ~25/30$, there are way better alternatives (including cheap dedicated). And if you need more bandwidth, cheap VPS tend to come with 20 or 100GB/month at least. But you'd get less RAM.