Julian wrote:
I'm inexperienced with network security and iptables
I recommend that you use ufw or Shorewall or something, then. Those will let you exclude SSH on 22 and HTTP on 80, and set up iptables for you so you don't have to learn it all. There's a lot of caveats to getting iptables right -- like not forgetting localhost, making sure RELATED/ESTABLISHED comes first for performance, and so forth.
Overall, security-wise, you need to allow ICMP through as well. I've never been a fan of selectively filtering ICMP, so I allow it all. Blocking selective ICMP traffic leads to weird behavior, like path MTU discovery failing (if you're interesting in Googling). Otherwise, yes, your description sounds reasonably secure.