Where can I find the cheapest house? I found a house near dragons reach for 5000 gold but I don't have enough. Also what is the quickest way to earn gold?

The Whiterun house (5,000 gold) is the cheapest in game. It costs another 1,250 gold to furnish.

Easiest way to make gold is dungeon diving. Because of the way the economy works (it's like Fallout rather than Oblivion in that when a trader buys an item, their gold decreases) I've found I've got so many items I want to sell it generally takes an entire trip round Skyrim before I've sold it all.

There's an unlimited gold glitch on youtube, just search it up. Do you happen to know if Gurdur's house is safe to store items in? She gave me the key when I and the other prisoner went to riverwood.

is the unlimited gold glitch on console or is it on pc?

Console.