You're only oxygenating the beer if you use a hand keg pump that pressurizes the keg with air. A handpump in UK parlance is a beer engine, used to pull beer from the cask to the glass. I think several people on here have used RV water pumps as a cheap alternative to beer engines. Beer engines are fairly cheap on eBay in the UK, but shipping to the US is a killer.
The difficult bit is the cask itself. Coincidentally I've just this second posted a thread on my plan for making a pressure barrel for cask conditioning beer, including a CO2 infection option from a Speidel fermenter. Alternatively, you can use a corny keg and a cask breather or regulator set very low to keep a blanket of CO2 over the beer to avoid oxidation - there are a few threads on this. You do want a small (controlled) amount of oxidation to get that cask beer taste though. Or you can spend $160 on a stainless steel pin or $99 on a plastic firkin from various online sources as the cask, remembering to also budget for spiles, taps and bungs. Ukbrewing.com is one source for these.