Dimity, this is a really great question. I think you might get as many answers as there are Fabbers, because we'll spend on what is most important for our climate/ lifestyle/ style persona.
I do think that Angie gives great advice, though, and I follow it. Not only are these things first on a style makeover, but they are things worth spending on:
Hair. (Great hair cut and regular upkeep)
Specs (if you wear them)
Foundation garments, esp. bras.
That is where I'd put my money first.
Next, for my climate (wintery) -- coats and boots. They cost a lot even if they are low end (relatively) but higher end will take you a whole lot farther.
After that, I start putting money into footwear. I do stalk sales for shoes, though, as well. I just never ever buy shoes that are cheap to start because they are never ever comfortable for me.
Around the same time in a wardrobe re-build, I would start adding a few pairs of premium jeans. But this is because I work from home, live a casual life, and wear jeans a lot. If I didn't, I wouldn't bother with that.
Then, tailored pieces like jackets. I love jackets, adore them -- but wear them a lot less than I might like due to weather/ lifestyle. However, a few higher end ones really give a good backbone to any wardrobe.
If you add higher end pieces a few per season, eventually, you have a wardrobe sprinkled with them from end to end. It is a process and one that takes some time. I'm now adding some higher end knits and shirts.