I'm currently only level 8 and want to build a house (the Falkreath one). I've got less than 5,000 saved up now, but would like to start ASAP, so I have room to store my crap at least. Can I start building small so I at least have a place to store stuff, and then continue adding on as the fundage becomes availabe? Or should I start saving up now? How much should I have saved up in order to build the house?

yes you can.

So I should just buy as soon as I can and start building? I was thinking about buying the Whiterun house in the meantime because I could use a place to store stuff soon...but that's kind of a waste of 5,000 if I can get a basic house built relatively easily in Falkreath just for storage

You can just buy the land and have a chest to store stuff, before even building the house. You are given enough raw materials to build the small house, which comes with another chest even before you furnish it. You could mine your own ore, kill your own trophies, do some wood chopping to get in favour with a mill owner and get your sawn logs for free. You want to be enthusiastic you could build the entire house for nothing, each plot comes with it own clay and stone sources. it is only with furnishing you need to buy a few things.

How much does the plot of land cost?