Actually setting that up will not be too hard! The only ting you may need to worry about would be the security on the office pc.
First of all I gather the ADSL router you already have is not wireless, so you will need an Access Point (AP) to have a signal for the students to connect to. Depending on the area you would like to cover you may need more than just one. You will also need some Cat5 (ethernet) cable to connect the router to the AP.
Once that is done you can connet the AP to the router and make a couple of changes in the AP configuration and you will be set. The AP setup is particular to the actual AP you have so I wont get into that right now.
The technical part is actually pretty easy. You would either use guest wireless if the router has that feature or you use a firewall rule if it has that feature. If it has neither than you get into buying equipment that does.
The legal issue is more your problem. You end up being responsible for misuse. Gets very expensive to try to prevent misuse. Teenagers in particular are going to use file sharing software to steal media. Will not be long before you start getting cease and desist letters from the RIAA and other places. You could also get the government coming in and seizing all your computers because some pedophile decided to post child porn via your connection. You are guilty until proven innocent in this type of case...even worse for the reputation of a church.
It likely is not worth the hassle. You would have to find a way to only let people you authorize use the connection which gets to be a support issue trying to setup and keep userid and permissions all correct.
bill001g is correct on the leagal issues involved.
To do someting like that you would need a "kiosk" type software something similar to something that would be used say at an internet cafe or hotel business centre type establishment. I'm not sure if you could find something like that for free though.
It is not just software you need a hardware device to intercept and process the traffic and authenticate the users. There are lots of ways to do this. Mostly this is a firewall.
I know one of the "cheaper" solutions comes from fortinet. Since there are many option you need to factor in its hard to select a exact product. Now the key advantage of buying commercial equipment is they have pre sales support engineers to help you select product. This is part of the reason commercial stuff is expensive.
This is not to say you cannot build all this yourself since there are free version of most this and all you need is a small server. The problem is it takes a high skill level to correctly install security things properly