2001 Toyota Corolla 3 speed automatic issues?

I'm looking to buy a car for my wife and one of the cars is a 2001 Toyota Corolla CE with 110,000 miles and has a automatic 3 speed transmission. Iv read things online (edmunds.com) that say it's "archaic" and should be avoided. I was wondering if anyone had experience with these cars. it is for my wife and she has never had a car or even driven much so she is not picky and so I'm not too worried about much power it has just its reliability. Also interested to hear from owners of one what they think