Should I bring my car

I would not bother, its a costly process, a lot of paperwork.

Thank you. Is there good transportation when traveling outside of lisbon? I have never been out of America

There is a good Train network in Portugal.

Children aged under five travel free; those aged five to 12 go for half price.

A youth card issued by Euro26 member countries gets you a 20% discount on regional and interregional services on any day. For distances above 100km, you can also get a 20% discount on intercidade (express) services and a 10% discount on Alfa Pendular (AP) trains – though the latter applies only from Tuesday to Thursday.

Travellers aged 65 and over can get 50% off any service by showing ID.

Don't bring your car. Sell it and buy another when you get here.

Cars are expensive in PT so it might be worth considering.

I have just done this exercise, but I drove my car over here from Spain.  Driving over from Spain is a different thing altogether than paying for shipping.

I got the tedious work done by an agency which specialises in this type of thing.  However, they do not speak English so you would need to take a PT speaker with you.  The agency ladies were brilliant.  The cost to me was amazing.  So much less than I feared and which I had read about on some internet comments.

Each case would be different as it all depends on the cost of the car, the age of it, etc.  One of the main documents you would require is the car's Certificate of Compliance.

I had to give the agency a lot of documents which they had a list of and which they knew I would need.

Apart from the agency charges, the car has to go over the pits and that cost me 70 Eur.

If possible you might be able to get an idea of the cost and the info you would require BEFORE bringing the car to PT because you obviously need to take into account the cost of shipping.

Outside of Lisbon you will need a car here in PT.
Some coaches are great and offer a good service.  From my town it costs me 5 Eur one way to go to Lisbon non-stop.  The service is frequent.
The Metro in Lisbon is very good.  However, the train services are not great and recently there were more cuts announced.  This website might be of interest to you:
https://www.cp.pt/passageiros/en

sorry it has taken me so long to say thank you to both of you for replying to my question. i have a 2018 toyato prius. i think i will wait till i am in portugal and know more about my surroundings before deciding about the car. for now the car will stay in the u.s. with a friend.