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You buy the house in Whiterun by becoming a Thane of the city. The Steward then offers you the option to buy the house for 5000 gold.

I prefer to hoof it to the towns the first time. You find all kinds of great locations along the way, gain a level or two, raise your skills, and earn some gold.

There is a manual for Steam. Go...

You can fast travel to cities. But you have to visit them first. Which seems reasonable to me.

One big change from Oblivion that perhaps you are running into is that the difficulty of monsters...