OK, so you've picked your race, sex, birthsign and class and you have a workable character. You've witnessed the Emperor's assassination, received the Amulet of Kings, managed to escape from the Imperial Prison, and are now standing outside the Sewer Entrance northeast of the Imperial City. You've got whatever you picked up on your way out and are ready to rock. Now what?
The answer to that question is "whatever you want to do." Seriously. As of the end of March (about 10 days after the game's release) I'm playing an 11th level character and all I've done (aside from the Recommendation quests for the Mages Guild so that I can get access to the Spellmaker at the Arcane University) is wander around the countryside. I haven't even started on the Emperor's mission to deliver the Amulet of Kings. I haven't done any quests for the Fighters Guild, I've joined the Thieves Guild and unloaded some loot to my fence, but other than that, I've spent my time exploring (and being turned back at the borders more times than I'd care to think about). I duck into every mine, cave, abandoned fort, Ayleid ruin or whatever that I can get into. Along the way I've bought a couple of the cheaper houses and some furnishings, unloaded all of the loot that I can carry on any merchant that I can find, killed a few hundred creatures and whatnot, got spanked a couple of times, diseased and cursed more times than I'd care to count and cured just as many times. In short, I'm being an adventurer. I'll get into the other stuff eventually (how else am I going to be able to write the walkthroughs?), but the whole point of this little discussion is to show that you're perfectly free to do whatever it is that you want to do.
I imagine that most players will launch right into the Main Quest, find the missing heir and "close shut the jaws of Oblivion." Others will head for their favorite faction. Others will do like I'm doing and just wander around seeing what kind of trouble they can get into. Everyone is going to do some combination of those at one time or another because this is an open-ended game and you're free to do whatever takes your fancy. OK, all of that out of the way, let's get into some of the stuff that will keep you alive long enough to do whatever it is that you're going to do.