Mmm, your right it'll cost something, though AWS free tier covers 15GB per month of bandwidth, then 12 cents per GB after that, so I'd expect it to be a few $.
Obviously though, there's cheaper options than AWS out there - Linode include 200GB of transfer per month in their $20 option.
I mostly just used AWS because I could start the server, build it, and blow it away, then restart, all without any hassles or full monthly chargers.
If you are going to host it for a long duration, you can reserve a heavy utilization micro instance and end up with an instance cost of less than $6.50 per month (with a three year reserved instance).
As long as you aren't serving lots of images, this will keep you well below $20/month - even with large amounts of traffic.
If you are serving lots of images, or worried about excessive bandwidth: Linode gives you 20GB/200GB (storage/bandwidth) on a 512MB server for $20, and MediaTemple gives you a 512MB server with 20GB/350GB for $30 (a little cheaper if you are going to be in the 300GB range when you consider Linodes .10/GB for overages).