You don't need a server, you need an Object Storage service, it's much cheaper with less headaches ... No server manipulation, No Hardware failure and No "bad" Support.
OVH Object storage
It's at $0.011 /month/GB of storage and $0.011/GB Outgoing traffic. Let's say you store 20 GB of pics and get about 3000 hits daily, assuming that each pic is 2mb, you'll need 5GB of bandwidth daily. The math :
$0.011 * 20GB (storage) + $0.011 * 6GB * 30 = $2.2
You can also checkout Backblaze :
http://backblaze.com/b2/ you get 10GB of storage for free (with 2500 operation daily, meaning, you could store your site's pictures, for free !) and pay as you go, it's cheaper than OVH, only $0.005/GB but it limits the number of operations.
AWS is great but it costs too much IMO.
If you don't want Object Storage and need a VPS, get an SSD with good I/O and 1Gbits WITHOUT limitations (read the TOS !! sometimes, you have 1TB bandwidth but only the first 50GB or 100GB will not be caped, the rest of the month, all the bandwidth WILL be capped).
If you don't need an IP address and can work with a NAT, just get one but pick wisely.
Let me know if you need any help.