"Oh drat! Just got a call from my wife. "
I have a 2000 Rx300 with 96K miles. Though clunking and loss of reverse sounds like transmission problem, stalling at stop lights sounds like a dirty idle air control valve, another very common problem on this vehicle. It's straightforward to clean it, but it's a little beyond what the person who just does oil changes will probably want to get into. Dealers won't clean it; they want you to buy new one for $400+ bucks. Contact your local reliable independent shop.
There's plenty of discussion on the internet about Rx300 transmission problems. I'd just add a couple of things. Consumer Reports surveys show transmission problems in this vehicle as being "average", which is a little worse than what we'd hope for a Toyota product, but not indicative of a dismal situation, as internet reading would have you believe. On the other hand, if it happens to you, of course it's dismal .
If the vehicle isn't dead, and you want to find out more, I highly recommend sending a sample of your used ATF to Blackstone Labs (http://www.blackstone-labs.com/index.html). They were reviewed in C & D last fall, and I've had them analyze my ATF a couple of times. Cheap yet comprehensive, and real people do the testing and communicate with you re results. They're happy to engage in some back-and-forth via email, and give their expert opinion :) . If you catch it in time, you can likely extend transmission life through more frequent ATF changes, and making sure the filter screen stays clean. I also recommend buying their pump for taking samples -- very well-made, professional-quality piece of gear that makes grabbing ATF and engine oil samples a snap.