The only reliable way to check prices is the AH itself. There is no API that allows to read out AH prices and parse it into another website, so all information would have to be gathered by hand, or by slow (and still bannable) scripts, and will hence be outdated.
How much prices can vary becomes apparent whenever there's a new announcement. Brimstones were at 10k gold for months, then there was a blue post saying "they're looking into making them more useful" and even though there was no concrete information and within the next few weeks nothing will happen to brimstones, prices went up to almost 100k. There's lots of fluctuation and a simple rumor on reddit can change the whole picture, therefore I would be careful.
You can ask for price check on single items and get some guesses by the community in several forums; haven't seen a price check request on this site in ages, though. If you spend a few minutes every day, you'll get a good feeling for most prices really quick, though.