What would you recommend to a firewall newbie for a firewall solution that can be handled remotely, maybe either by ssh or the browser?
tl;dr - Learn iptables.
There many iptables wrapper scripts that you can use, but all of them have their own syntax that you're going to have to learn. As long as you're learning something, it might as well be something that will be universally-applicable to any linux server you touch now or in the future.
Take the time to learn iptables' native syntax. It's quite simple, especially if you only need to do a default deny with a few ports to open.