would it show my custom domain name in the address bar, or redirect and show the free Google site?
It would redirect and show the google address in the bar.
Sounds like with your usage that you just need the most basic hosting package available. 19Mb of storage and the amount of page views you have are both easily covered in the most basic hosting you can find out there.
This may be a little outside your comfort zone, but you could even easily host that on your regular adsl/cable (not dial-up) Internet connection if you had a web server that was up permanently and bought a domain name at DynDNS and pointed it at your IP address. In terms of hardware you really don't need a lot, $100-150 could get you quite far. You would however need some knowledge of how web servers work <img src="/ubbthreads/images/graemlins/blush.gif" alt="" />