My society runs recball sessions every 4 weeks and from the pool of 35 members or so who have paid a membership that attend these, we then bring people forward to work with on a more competitive level. The key to our success is just simply the number of people we get through the door. Since you've probably missed freshers week you will need to work hard at getting your society name out there via emails to student groups, advertising on the uni student website, TVs etc. If there is any opportunity for societies to set up stalls somewhere on campus i would do this, for example outside a library or something, anywhere with high traffic to make people aware you exist.
As for the running of your society, just get people to make some sort of financial commitment so they will want to attend and get their moneys worth (i.e. a membership) and run regular days at a local site. You are looking at taking a large group booking so if you don't have a good relationship already with a site, then you do have some bargaining material.
After a few events, try and get the word out to these guys about the possibility of a competitive team. If you have 5+ members wanting to do this then approach the uni with your plans and try to explain what your aims are. If you have separate funding for sports teams then try to find out the requirements for this since sports funding is usually far more substantial than society funding, but also is harder to get. From here, just assess how much money you have as a club, and how much people can commit themselves to buying their own personal gear and just try to make it as cost effective as possible. For example at Glasgow members are to pay for their own personal items like masks, packs jerseys etc. but the uni provide the marker setups.
The hardest part is getting skint students to front the cash to buy the actual gear, so anything you can do to overcome this challenge will help out the most.