Hot spot is used for that. Ot has the option to offer user login page before letting him access Internet, but you may tweak it to autologin, having effect that user must see your page ant then access internet.
Without hotspot, you may try this:
if user’s IP is not in “active_internet” address list redirect him to your site, and put him ont that list but using expire option so use will be automaticaly removed from the list after specified period of time. If user is on the list do not redirect him to your page but let him access internet.
this is just an idea, it needs soem polishing, but it may work.