I was waiting to see if anyone responded who was recently there, as I travelled up and down Portugal the summer of 2013. I can only offer my experience as to that trip.
We rented a van at the airport for our 3 week trip and did use the "new" highway system. All the tolls were automatically paid by the rental agency and of course were charged to my credit card. No problems at all and no worries. However, my niece rented a car from an off site agency (her car was not equipped with the toll transponder) for her 2 weeks with us and if she used the "new" highway system, she had to go to a local post office within 48 hours (I think) and pay the toll in person...headaches and wasted time! Check with the rental agency if they provide the toll sensor in their cars and avoid this issue.
The GPS issue is a different story. I have a TomTom, with a 4 year old Europe map, and only had some minor issues. All the highways and signage is quite good in Portugal, so for me as long as I was heading in the direction of my destination I felt fine. The cities and towns worked great for my older GPS map. If I did jump on the newer highway system, of course my GPS did not recognize it, but I used common sense where I needed to get off. I would do some more research on the Garmin website or maybe call them and ask. With the maps in the Rick Steves Portugal book, I think you are fine, but it will depend on your definition of "fine". :-) I also had his Spain and Portugal folding map which I highly recommend even with an up-to-date GPS map...it also came in handy with his book.
One last note: be cautious if your GPS wants to send you down what looks like a narrow road in a village or city...Look for an alternative because that narrow road could get even narrower and you may end up having inches on either side of your car. This happened to me and I was driving a 9-passenger van! To say the least, I had never been so nervous driving in Europe, but I luckily got out of that jam with no scratches or dents. Lesson learned and I am passing it on. I hope this helped a little at least.