Eric, in the US, you can get a uric acid meter, which is the fastest and most economical way to do uric acid testing, but you have to order from amazon or something like that as US drug stores don’t carry these. You can also pick one up in the UK if you are fortunate enough to travel there occasionally. These are also commonly available in Asia.
Most labs don’t support self-ordered tests, which is dumb, but that’s how it is here in the “land of the free.”
As to beer vs. wine, wine is generally low in purines, so provided you don’t drink to excess and do stay hydrated, I think wine is a better choice as far as gout risk goes. Beer can be quite high in purines, but it is very difficult to know the purine content for a specific beer, especially the tasty local brews for which no data is available. I have found that for me personally, I can’t have both beers and a high meat meal without risking a flare, so for me it is one or the other, but not both! I can’t overstate the importance of water when consuming any alcohol.
Good luck and let us know how it goes with a meter purchase here on the forum.