Let me start off by saying that I am an Italian-American, not a drop of Polish blood in me; so I'm not really in sync with Polish traditions.
With that said, most of the recipes I'm seeing make it clear that you want to use a light beer, so obviously you're not gonna want to use a stout or porter here (though I'd be curious how it tastes; my friend swears by Guinness in his beef stew). With that said, most lagers or pilsners (a type of lager) should be fine for your purposes (of course I would avoid macro-lagers like Bud, Coors, and Miller because they are awful). Anchor Steam Beer might be interesting in the soup as it packs a lot of flavor for a lager type beer in my opinion. For authenticity, you're likely gonna want to use a pilsner. You have to realize, as the Wikipedia article points out, that until the 1840's or so, most beer from the area was top-fermented (like ales; modern pilsners and lagers are bottom-fermented) and the taste varied widely, so I'm not sure how a beer 300-500 years ago would have tasted. The closest you'll likely be able to go back is the 1840's; in which case I'd give Pilsner Urquell a shot as it's the first pilsner beer in the world. Victory makes a mean pilsner (Braumeister Pils) too. Unfortunately it's draft only, so if you have a growler handy you can use it; otherwise best look elsewhere. Of course you can probably get away with most Czech pilsners. I can't figure out why Beer Advocate doesn't have a sorting option so that you can sort based upon the rating, but I digress.
You have to remember that beer was much different 300-500 years ago. Yes, there are some breweries such as Dogfish Head who recreate ancient ales. Yards has also recreated three brews based upon George Washington's, Thomas Jefferson's, and Ben Franklin's (my favorite of the three) original recipes. But for the most part, beer has evolved in the last 300-500 years; even in the case of the Dogfish Head and Yards brews I mentioned since they have to be pasteurized and must meet the (stupid) FDA standards here in the US. If you've ever tried raw milk, you know how much pasteurization changes the flavor; same goes for juice and beer.
With that said, lets go back to the whole top-fermenting thing. You might want to give a grätzer a try as well. It's an ancient Polish beer which has been recently making a comeback. There's a project going on right now to recreate the brew. However, since the brew is so (recently) new, I'm not sure how available it is; you'll likely have to make a trip to San Francisco to get some. There are others too, such as those offered by Westbrook Brewing Co. and Schlossbrauerei Au. But I'm not sure how readily available these are either. You're probably better off brewing this once yourself until this beer is pulled off the "endangered beers" list. Yards has also experimented with this style, but again, it's not readily available (see Tadeusz Kosciuszko Smoked Pol)
This website may also be of use to you; it outlines a history of Polish beers.