not so sure about the gay scene in berlin. but if you are keen on the general touristy attractions and so on, this reply would help a little.
the last time i was there, my main motives were to see as much architecture and culture as possible. so my favourite places were the museums on museum island (particularly the archaeological museum, hire a guide if you can and see what were destroyed in WWII and how they repaired them). not far from there, you would also see a huge church with a dome. walk along unter der linten and you will end up in potsdamer platz.
I really like kulturforum too which houses the Berlin philharmonic, the national gallery as well as the sony centre. (potsdamer station) when you are done here, make your way to the reichstag, which is the parliament. along the way, you will see the Jewish memorial, the bradenburg tor and unter der linten (famous attraction). and finally the reichstag, which features a huge glass dome on top. it is a free admission attraction, but security is tight, there you get to see berlin from an aerial view.
if you wanna see more of berlin, on the east side, there is a long stretch of berlin wall with loads of great art work on the wall. i was told that somewhere here also has the best gay club (though i am not sure the exact name and location).
as for low budget shopping, there is a stretch of road which i believe is from
for luxury shopping, got to Französische Straße. and somewhere there, ask around for the RITTER SPORT chocolate shop, there you can custom make your chocolate which is great for souvenirs to bring home.
Hackescher Markt also have lots of shops for shopping and some of the best kebab i ever had. look out for little lanes and alleys with lots of graffiti, sometimes there is a bar hidden in the corner and it is quite nice chill out place.
travelling in berlin is not very cheap, i would suggest a 3 day ticket or a week ticket for the rail. or if you travel in groups of 5, you get cheaper fares too. walking in berlin is not easy as it is a huge city.
i am just sharing my experience in berlin, this is not an official guide. i hope this helps.