I'm another slow starter. Others complain about tutorials. I'll often do one more than once to get comfortable with mechanics before I begin exploring. In Morrowind the first thing i did was read the history books in the Census and Excise office. In Oblivion I picked a couple mushrooms and gathered a few Flawed Pearls. Sadly, my bags were full so I needed to head into town more promptly than I would have preferred.

I go out exploring.
I remember how I could have skipped parts of the mainquest with this in Fallout 3 (had the possibility but didn't do it though). I felt pretty lonely in that game. Withe the ambient music in the background & everything destroyed; surprised what awaits you over the next hill...
But I think that is always the best part in sandbox games: When you're still unsure/clueless about the game's mechanisms.

escape execution and then go to armourer and weapon smith

If you think about what it would be like in RL to find yourself in an unfamiliar place without the items you may need for survival...well, it's what I'll do. If I'm in a town, I'll be needing some $ so I'll look for work. If I venture out of town, I'll be needing to protect myself so I'll need combat items. First thing I'll want is a bath and a good meal though because I've just been in prison and probably eating garbage food. I'll just take it from there and talk to people and see where it takes me to find the things I'll need for whatever comes later.

:tes:

I'll do what I always did when I play a TES game for the first time.
I'll smoke a Joint before I start and then be overwhelmed by the stunning looks. Maybe laugh at the looks of some NPC's

You approach it from the side.

I'll probably spend the first hour taking in the scenery. Then find the closest town and spend an hour there. Once I'm at that point, I do a mix of exploring/quests. Main quest will be either entirely incomplete or partially complete until I'm almost done with the game.

I make my way to the nearest town or settlement so that I can get food and shelter. I talk to everyone there, and then branch out into the surrounding wilderness until something leads me to another town. (Like a quest)

I'll create two characters, with two sets of saves right away. A stealth-type, and a warrior-type.

I'll play them each through the intro, and possibly the first dungeon or quest. This lets me get a feel for each archetype, and any new control scheme that's changed from the previous game. It also lets me see if I missed anything (like chests, secret passages, loot, etc.).

I did this in Oblivion to get a good feel for what I wanted to play. But with Radiant Story, I might hop back and forth between my saves throughout Skyrim so that I can see the differences in the dynamic quests.