I know that some people will do different things with different characters, but I can't be the only person with a sort of early game routine they do for most characters as you leave Helgen.

Generally, I hit the bandit camp, Talos shrine and Guardian Stones as I head for Riverwood. I then buddy up with Faendal + loot his house and Ralof's, selling all the stuff I find. I then head to Embershard, get that done, sell the loot and go to Whiterun. I do every single quest I can, make a bit of money and then clear every dungeon in the Whiterun hold (most of them, anyway). When that's all done, I'm usually like level 5-10, with up to 10,000 gold and some nice gear. Then I start a questline that fits my character.

This does get boring though, so recently I've been going to different cities and doing the same kind of routine but not in Whiterun.