Buying traffic in general is a very niche/expert thing. You can blow through, on average, 20K while you search for that profitable balance between cost, offer, etc.
Not knowing what this free site of yours is - is it simply a lander that moves the surfer onto the offer/main site or is it intended to be the actual sales page? - it's hard to set a budget or even expectations. But if it is a tube site, a porn list, something that a surfer would bookmark and be unaware of without the traffic re-direct then you might get some traction there.
How long term is your strategy for the site? Are you looking for an immediate ROI or looking to build bookmarkers/visitors over time? All these things need to be considered.
Great good luck!!