Getting in Good with a Wizard
Now that we have wrapped things up in Riverwood, it is time to return to Whiterun and score some points with a certain Wizard... So fast travel directly to Dragonsreach and head inside to revisit with Farengar, who is very pleased with your success -- and introduces you to his colleague who it seems was the source of the location for the stone.
Things now move quickly -- a guard comes in to report that a dragon has been seen and is attacking the city -- and you are asked to come with the Wizard to see the Jarl, who after being briefed rewards you (and the reward includes permission to purchase a home in the city! Nice!) and then asked you to accompany his Guard Captain to the gates and help with dealing with the dragon. His logic is you are the only one present with experience with dragons, so it sort of makes sense, right?
You unlock the Achievement "Bleak Falls Barrow" (10 GS) along with getting your reward, so good on ya!
When you reach the Western Watchtower you find Irileth near the gate where she is firing up her troops before heading to the Tower where she orders you all to spread out and search for survivors. As you search the dragon reappears and attacks -- and you join the guards in attacking it!
Your First Dragon Battle
As it starts to die its soul rushes into your body -- revealing to those present that you are a Dragonborn! Equip your shout and use it!
You now unlock the Achievement "Dragon Soul" (10 GS) for absorbing the dragon's soul -- and you have proven that you are one of the chosen -- far out!
The Only Good Dragon
Head back to Dragonsreach and report in to the Jarl, letting him know what has happened. As you explain it the Jarl is very pleased to learn what you are -- and tells you about the Greybeards -- and you learn that they are summoning you to meet with them. It seems that you will need to do that, but before you do we should wrap up something here...
Head to the Wizard's Chamber and use the enchanting machine to disenchant. You should have the Axe of Cold from the Barrow, and a fire-resistant shield as well as the Axe of Whiterun in your inventory -- I chose to hold on to the Axe but to learn the enchantments from the other two, which of course destroyed them...
Now talk to Farengar -- wake him up if you need to -- and learn what he can tell you.
--== Purchasing Your First Home ==--
If you have been following the guide and looting every valuable thing that you can, you should have nearly 10,000 gold by now -- and as you have permission to buy a home in the city, and as you have the money, it is time that we take care of that small task because it really is a major advantage in the game to have a place you can store your stuff!
After the Jarl declares you hero of the city, speak with Proventus Avenicci to learn what he knows about the Dragonborn and the Grey Beards and then pay him the 5,000 gold to buy a house in the city. This will unlock the Achievement "Citizen" (10 GS) and get you the key to your house. Next you should tell him you want to decorate your home -- there are a bunch of options including:
-- Alchemy Laboratory (500 gold)
-- Bedroom Furnishings (300 gold)
-- Loft Decorations (200 gold)
-- Dining Room Decorations (250 gold)
-- Living Room Furnishings (250 gold)
-- Kitchen Furnishings (300 gold)
After you buy the furnishings change the active quest in your list to Miscellaneous and Visit Breezehome, your new house, and then go there! On the way out you meet your Housecarl Lydia -- ask her a few questions to learn what she knows -- if you have never seen the concept before, a Housecarl is sort of like a personal majordomo who keeps an eye on all your stuff but also serves as a shield-brother when needed.
If you already have a companion you do not have to select Lydia to be it -- I kept the one that I have, Uthgerd the Unbroken. Lydia will be at your house whenever you want or need her -- and there is a bookshelf in your Alchemy workroom you can store your books on as well as other containers for you to store stuff in. Now would be a good time to store your ingredients in the Alchemy room -- and now that you have a place to store them, collecting any you find makes sense!
You should be at Level 7 or so at the moment -- and taking this opportunity to clear away as many of the Miscellaneous Quests as you can would be a good idea... I am just saying. The journey you are about to take is long and dangerous so having the levels and best kit you can would be good!