What is the first thing you do after escaping from prison and exiting the sewers? Is there a particular quest you like to start with or a special dungeon you head for immediately, or maybe a free item that you pick up straight away.

I am still playing through the game for the first time but already thinking ahead to how I will play next time.

Take a bath in the lake right outside the sewars. Then go home. Then join the local mages guild.

Swim across the river and attack the bandits while pilfering the jewels from the nearby jewellery box.

Offload/sell the junk from the starter in the IC market distrct - the unowned bags there are safe storage. Then take everything useable/sellable out of the crates, sell it, buy starter spells from Edgar, maybe train a bit. Deliver the amulet, join fg and mg in Chorrol, take the free goodies, sell most of it back, make the rounds of the mage guilds and do the recommendation quests. Whew!

For funsies, my last couple of characters have gone into Timberscar and retrieved the goblin totem staffs. They're uber weapons at lvl 1, hitting for 20 shock damage a pop, and have quite a few charges.

Mara

It depends on the character. I tend to play three or four characters "in parallel," and they're usually very different, with different agendas. Some of them advance through the "usual" quest lines, while some of them tend to go off and attend to their own business. I have one character, who aspires to nothing more than collecting ingredients, making potions, and selling them around the empire. He's very good at it, and occasionally I load him up and play his "life" for an hour or two.

I always play through the whole tutorial, even though it's "boring" by now, in order to get to know my character. By the time we get to the end of the sewer, we usually have an "understanding" of where we're going next.

There are a couple of mod-based "goodies" (as well as a few valuable vanilla items) hidden in Vilverin, which some of my characters will go fight their way through. On the other hand, one of the characters that I initially thought was going to do that surprised me completely, and insisted on heading off to the Priory without even stopping to talk to anyone, and ran through the first few parts of the Main Quest before even reaching level 1.

It can be a wild ride.

OMG I thought I was the only one who did this! Only with some of my characters though (mostly female.)

My next priority after hygiene is going up to the market district to sell all of the crap that I carried up from the tutorial dungeon. While in town I might do a couple of quests like the thorinir one or the one with the corrupt guard. I'll also join the thieves guild if it's suiting. After I'm done in town I head on toward chorrol to offload the amulet. That's when the game really begins for me. I usualy join either of the guilds, depending on my character and do the quests for that. I make a point to never take the free stuff from the guilds unless I'm playing a thief character. Even then I try to act like I'm actualy stealing it (make sure no one's looking.)

Getting the totem staffs at once was a good idea, usually gets them during the mage guild membership run. They are very nice at low levels and also sells for a lot of money then they run out of charge.
Does somebody not clear out the storage in the marked district the first day?

I always dump the Emperors bling on Jauffre then begin whatever I want to do, depending on the character.

Sell tutorial dungeon loot at Imperial City, go to Weynon Priory, give Amulet of Kings to Jauffre, grab Weynon Priory Horse + all the stuff you get from Jauffre, sell stuff you get from Jauffre (unless it's something useful), proceed with character-specific plans.

Sell all the crap from the dungeon.
Then start making my rounds of the cities, to receive my recommendations for the mages' guild.
Sometimes this takes a while, as there are caves and forts and the like along the way.
Then depending on the character, they decide whether or not we are going to do the Main Quest. If so, I start helping out with that around level 25 - 30. If not, I'm perfectly content with that decision as well.
I tend to use the Shivering Isles, as a test later in the game, to see if my characters' morals and values change, thus opening up additional quest lines and the like.

I usually go to see Jauffre, both to ditch the amulet and get some free equipment. Then I grab the fine steel longbow near fort Nikel is I play an archer (which I usually do). After that, mages guild.

i try to murder some poor, innocent soul to feel powerful and evil early on.

I never clear out the Market District storage. My character usually enters the Imperial City a little bewildered and wary of the whole guard/prison time thing, so he/she is afraid to loot anything, even though it seems like the stuff is public property.

Clam fishing!

I don't bathe in the lake - well not so close to the end of the sewers, anyhow - but the pearls in the clams are a useful addition to the initial wealth, with a high value/weight ratio. I usually have to kill at least one mud crab during that process, but that's the only thing to defend against. Hiking into the city usually gets a wolf pelt or some venison (depending on character skills), and sometimes both. Different characters will take shorter or longer paths in, and seek out or avoid conflict as they do so. Some may visit Vilverin, others Sideways Cave, most do neither.

The character usually has hit their encumbrance limit before they hit the Market District and has dropped some of the lower value / heavier stuff. Depending on what they need as initial equipment, there may be a bit of retracing of steps to go pick that up, too. Regardless of build, there are spells, repair hammers, and a more character-appropriate outfit to buy with the proceeds of selling the junk. Mages need more spells, fighters need more armor, but they all need something exchanged from the eclectic assortment provided by the introduction, so they all go into the IC and shop.

I would only head out from IC when the spells/armor/weapon situation feels "adequate" for the journey. By that time the character has one, character that is, and things take their own path.