All posters have made good points (check with local environmental regulators for available data, be careful of drawdown effects, put in well between your well and those at the landfill, etc.) Something to consider is that deep (or confined aquifer) flow can sometimes be contradictory to shallow (or unconfined aquifer) flow. Presumably, the well you are putting in is a domestic well and will therefore be in the deep or confined aquifer. In some cases the fissures groundwater travels in can be equivalent to pipe flow so that while a contaminant plume in the shallow aquifer may appear to dissipate laterally to non detectable concentrations a “safe” distance from your well site, it may be slipping into your drawdown zone via the deep aquifer. Hopefully, available data includes an examination of the deep aquifer as well.
As to your original question, if budget was a concern and I could just run one test I would analyze the groundwater in your well for EPA Method 8260 volatile organics. This method targets common volatile organics in fuel, solvents, household products, etc and can detect very low concentrations of these compounds. Also, some of these common volatile compounds such as acetone are very soluble and therefore more mobile.