Now that you’ve escaped the collapsing fortress and the dragon attack, you’re stopped by your companion, be it Ralof or Hadvar, who crouches behind a stone and watches the dragon fly off to the Northeast.  Hadvar tells you you ought to go on without him (as does Ralof), and you can- but you may miss a few things.  Incidentally, where Ralof gets you in with Gerdur, the woman who runs the sawmill in Riverwood, Hadvar lets you into the house of the blacksmith, Alvor.  The primary difference here is that Alvor’s house has more money in it that you can take, and an extra ingot of iron- and Alvor allows you to take some of the supplies in his blacksmith’s forge as well.  Gerdur’s house has a bit more food and clothing in it, and she lets you harvest from the plants in her yard during the daylight (otherwise you’re reduced to thievery, probably at night).

The path down the hill that your companion follows is littered with thistle, mountain flowers, and occasionally mushrooms.  And if you follow your fellow escapee, you get some additional benefits.  First of all, you can talk with the person you escaped with in order to learn more about the setting- the two have very interesting, differing views on what’s going on- and both of them are ‘right’ about the situation that Skyrim is in.  While Ralof encourages you to act however you feel is right and perhaps avenge yourself on the Empire for your arrest and near-execution, Hadvar will point out that while, as far as he’s concerned, you’ve earned your freedom by helping him out, other officers may not see it that way, so you should be discreet until you can get to Whiterun and talk to the Jarl.

The second direct benefit you gain from following your companion is that he leads you right to a set of Guardian Stones- and while you’re there, you can define your path- that of the Thief, the Mage, or the Warrior.  Whichever path you choose, you learn skills of that type 20% faster, so make sure you stop by there even if you choose to separate from your co-escapee.  If you don’t feel you need the background information or guidance, feel free to wander haphazardly down the mountain- the only enemies you’ll find here are the occasional wolf and a small camp of bandits who leave you alone if you back off after you approach them.  Or you can kill them and take their stuff, depending- their camp does make a convenient storage/camping site if you come back to the area later, and has a number of containers in it that can hold things for you, as well as a little food and some dishes.

If you are following a companion down the road and you take a few minutes at the Guardian Stones before selecting your Path, then you’re probably going to run into some wolves down by the river- this is a good chance to snag their pelts to make leather with, though there’s a minor risk of catching a disease if you do poorly enough at fighting them.  If you want bow practice, you can usually spot a rabbit or two from the path, though you have to be quick-acting or your friend will get ahead of you and stop talking to you.  Don’t get too worried though- they’ll show up in Riverwood within a day or two.

Finally, on arriving in Riverwood, you will be led into Alvor’s house and get to hear a bit from him about his perspective on the war- the blacksmith is an eminently reasonable man, loyal to but not fanatical about the empire (just don’t hurt a chicken while he’s outside or he’ll crack your skull open).  He suggests that you head to Whiterun in order to let the Jarl know about the dragon, so that the Jarl can send some soldiers to reinforce the area.