I have read this question and done some investigation, and I want to make sure I have some of this right.
If I have a server somewhere where I can install bit coin (I'm thinking bitcoin-qt on Ubuntu) then I can run bitcoind on that computer.
I could setup a http server to accept requests for a new bitcoin address from bitcoind and return one to my other web app (hosted on Google App Engine).
Then as I understand it, if I setup walletnotify, it will automatically call my scripts to process payments that are received.
I'm thinking I might be able to get away with putting this in a friend's living room, though I'm not entirely sure I will have a static IP address, but maybe I can work that out.
I realize there are 3rd party solutions for this, and this is a broad question with many ins and outs, and I should be more knowledgeable of Bitcoin and hosting my own servers (as the PaaS solutions don't seem to let you run bitcoind), but do I have that mostly right or is there is something amiss with this endeavor.