The only thing I discovered after browsing through that site is that I am too poor to own art.
Of course, well known artists will command serious prices, but for every well known artist, there dozens of other lesser-known artists with comparable quality and styles that you can get a lot cheaper.
Or commission your own art if there's something specific you're looking for. Once again, if you're looking for something down by a specific person, you're going to pay for that brand, but if there's a styler you're looking for, you should be able to find someone to do it for a lot less.
[1] https://www.quora.com/What-are-some-strategies-for-buying-ar...
Some of them he couldn't even give away!
Seriously though, if you want cheap art then visit some art student graduation shows or visit the cinema. Amazon has probably moved into this area because it is high margin and they'll get a big cut and compete with eBay, not through any desire to democratize fine art, so I doubt they'd want the prices low.
Group shows at a small gallery, or benefit auctions for local arts-related organizations are another idea. You can get access to more mature work that way.
You don't generally want solo shows at galleries, but at group shows, people will show smaller works. You have to be well-informed enough to know the gallery and their artists, of course.
Benefit auctions often feature works that local artists have laying around in their studios and donate to the auction (partly for the tax write-off, although that is monitored now). You have to be confident of your eye, and choose the right auction, one that is connected to local artists with actual talent.
All of the above requires footwork and an independent interest in contemporary art. This disqualifies 99.9% of people.
Often a single collector or gallery will make all the difference for a young artist. One single person that buys enough of their art for them to make it on that part-time coffee house job and still pursue their art.
Disclaimer: I am dev/founder of A&C
Outside of this site, there are studios in China which will replicate pictures or paintings quite affordably - I have a 2000x1000mm copy that cost more to stretch than commission (The original: http://luxxurylivving.com/wp-content/uploads/2010/12/Francoi...).
Another option is to hit up student exhibitions at high school or college level and find rough gems.