1. As opposed to what? Shipping your bag? Of course you carry it on. There are luggage racks at the end of the cars for larger suitcases, and the smaller stuff can go above you or at your feet. You have elevators/escalators both at Porto-Campanhã and at all Lisbon train stations. Mind the gap between the train and the platform, it will be a small step up into the car.
2. If you're very concerned, bring a cable and a lock. IIRC Alfa Pendular has a luggage rack with wire that you can pass through the handles and a lock (image). There have been cases in early 2015 of people stealing bags, then they were caught in mid-2015, I haven't heard anything since, but YMMV.
3. Define best? You have many options on both ends: metro, buses, taxi, uber, ...
For whatever reason, I haven't seen pickpockets or bums outside Portuguese train stations or airports.

The only reason to take Ryanair is if you're really sensitive to price (there's very little reason to take TAP, unless you're going to/coming from somewhere close to Porto Airport). The train is faster door-to-door from city center to city center.

I will also mention that there are buses, which cost a bit less than the train, but take more time.

Also, read the sticky on PT trains in this forum. If you buy your tickets online a few weeks in advance, you can usually get a nice discount (10-15€ instead of 25-30€ each way).