I put aside my first playthrough (Orc, heavy armor, 1-handed, destruction) to start another one (Wood Elf, Archery, 1-handed dual wielding, Light Armor, Stealth). I'll come back to the first playthrough later to finish the Companions and Mages College.
After looking at the house options, I decided to pass on the one in Whiterun and save my money for the one in Riften. It seemed like an easy one to get, and there's more stuff you can buy for it. I go as far as killing the first dragon in Whiterun, then head out to Riften (via Windhelm to start the Dark Brotherhood). I do the two quests that the Wiki said have to be done to get the house. I have the 5000 gold for the house. And...nothing. After a closer look at the wiki and guidebook, I realize I have to do quests for people in the town before I can get the house. So I fast traveled back to Whiterun to buy that house (to store all my crap) and started working on the quests for the people of Riften.