I would start it, run with it, watch the load and bandwidth, increase your plan as necessary. I wouldn't get too over-the-top with ordering a bank of servers until you have the concept working. The Rsync/Round-Robin DNS can come much later.
You can embed the affiliate's url in there with a mod_rewrite, something like:
Surfer sees:
http://site.com/fhg/affid.html
You code for:
http://site.com/fhg/index.shtml?affid
Your .htaccess (or preferably put in the config) would be:
RewriteEngine on
RewriteRule (.*)\.html$ index.shtml?$1