[...] Preferably such as enables the installing of a really good web browser/the Android app store?
Keep reasonable expectations for browsing. The NST runs Android 2.1 eclair, which is rather old. Don't expect Firefox or Chrome. Opera Mobile works, but it's not a fantastic browsing experience. More "usable in a pinch."
You'll need to use Search Market to search for anything in the Google market.
I've been putting off updating to 1.2.1 simply because I don't use the B&N reader. Looks like NOOK Touch ModManager will let me redefine the side buttons, so my last excuse for not updating is gone. Now a NSTG looks more attractive.