I just came off a three-week trip to Europe and I stopped by the Czech Republic, which is where people supposedly drink the most beer per capita in the world. You could call it beer heaven, too. The neighboring countries I visited, Hungary, the Slovak Republic and Poland, aren't exactly slouches when it comes to beer as well. So many different brews, and all so darned cheap! You could buy them off gasoline stations for less than EUR1.00.
I've only started as a beer enthusiast myself but I've been lucky enough to sample quite a few brew styles (no 14% abv India Pale Ales yet though). What I've noticed so far is that the style of the beer doesn't really say much about its bitterness per se. For example, I am a huge fan of dark/dunkel lagers and none of the ones I've tried have ever been bitter; if anything they're some of the smoothest tasting beers around. In contrast it's the light-looking pilseners that have tended to be deceptive in their bitterness.
Non-bitter stuff I'd recommend, in no particular order:
1. Hefeweizens: Of these unfiltered special wheat beers, I've tried Gordon Biersch and Hoegaarden. Both are great, but GB's tastes a little heavier on the tongue.
2. Dark or Dunkel lagers: San Miguel Cerveza Negra (aka "San Miguel Dark Lager"), Kozel Dark, Soproni Fekete Demon, Super Bock Stout - all are pretty good.
3. Pilseners: The granddaddy of this style, Pilsner Urquell, is my favorite. Soproni is a close second. Both are smooth and drinkable. Soproni has just a bit more bitterness but definitely not enough to screw with your palate.
4. "Adjunct lagers": Seriously, if you want a non-bitter beer Corona Extra should be on top of the list. Throw in a lemon slice too.
5. Have you ever tried any "lemon beers"? Those are definitely NOT bitter, although those also taste closer to Mountain Dew than beer. Want examples? I've tried Super Bock Green and Bazant Radler.
Ad astra per aspera.