I think for most of us, the best part of playing Skyrim is the mental roleplaying we do along the way. We either make the character some ideal, best-in-Tamriel version of ourselves (which is a good place to start with a first character), or we devise really complex characters with intricate backstories and goals.
The first time through, the closer you can play a mentality like your own, the more meaning you'll pull out of the story. I also recommend reading every book you find.
As a word of warning, because we've all experienced it; you will end up with quest items in your inventory for life. Skyrim has always been plagued with bugs. Some of them are as simple (and annoying) as picking up an item before the quest has been assigned, and others are a little more participatory, such as killing the person you need to make a delivery to before you made the delivery. Luckily, quest items have no weight in your inventory, so they don't count toward your carry capacity (the full amount you can carry before you walk ridiculously slowly, and can no longer fast travel).
You definitely found the right community, though. We absolutely favor character playing, and exploring different build types (build type being when you place restrictions on yourself, such as what you can pick up, the kind of armor you wear, the fight style you employ, and places you can and can't go to achieve an overall effect, such as "Robin Hood", or "William Wallace in Skyrim") over power gaming and level grinding.
Though, if you do want to level relatively quickly, it's not too difficult. If you pick up alchemy pick every flower and bug you see, and use a potion guide
like this one, where you type in the ingredients you have in your inventory at the time and it tells you the most expensive potions you can make with the ingredients you have. Rather, all the potions you can make, listed in order of monetary value. It definitely strips away some of the immersion (or a lot of the immersion), but many people get tired of having to rebuild their potion recipe library for each new character, because (rather understandably) you start every character knowing no recipes at all. Or even ingredient properties and interactions. So it ends up being a trial and error thing, which does make sense from a mechanics and role playing stand point, but is, again, frustrating from a multiple character stand point. (Though I doubt you're near a multi-character point in your budding obsession with our favorite time sink.)
In short, with all things in Skyrim, value = experience. The more damage you cause with a Destruction spell equals more experience earned. The more HP you heal with a Restoration spell, the more money a potion, piece of jewelry, or suit of armor is worth, the more experience you gain for making it, and selling it.
But, in terms of personal value, the more you put into it, the more you'll get out of it. So don't hesitate to really let yourself go and become your character.
Hell, write about the adventures you have. Tons of people have been inspired to write fiction based on their characters and adventures. You're welcome to share such things with us here. Just make sure to keep first person journal entries that follow the linear story of the game to your blog (helpfully provided by the forum here), and anything that doesn't necessarily follow the literal events of the game (but which may still incorporate the narrative) can live in the fan fiction section.
Unnecessary announcement: I have hiccups that won't go away.
So, I'm going to go drown myself to deal with this. You enjoy your Skyrim, new friend.
P.S. You're only two years older than me, and legitimately far from the oldest person on the forum. So, "older newbie" doesn't really apply.