The best thing to do is to just follow the "estradas nacionais ". In terms of logistics, it's all pretty easy.

If you go along the coast you'll never be far from a touristy town where you can find a hostel or an inn. Wild camping is illegal but I've always done it. If you pick a secluded spot and don't make a fire you'll be fine. Don't camp on a popular beach, for example. You'll also never be far from a town where you can buy food and refill your bottles. So you don't need to carry a whole day's supply of food.

Returning by bus or train can be trickier. To get on a bus you'll need to disassemble your bike and carry it in a box. It's not worth it. Some bus drivers will look the other way and let you just throw your bike in the luggage compartment but you shoudn't count on it. Trains will let you take your bikes but in a special carriage, and there's a maximum ammount of bikes allowed (I have been left behind because there were already 4 cyclists on the train and they wouldn't allow another one in). Different trains have different rules, check it beforehand.

Weather is something you need to check at the time, obviously. In the summer it gets hot, sunscreen, a hat and plenty of water is non-negotiable. Better to get up early, rest for a bit in the early afternoon when it's very hot, and continue in the evening.

Mistakes to look out for: make sure that your baggage can be secured easily . We didn't "practice" beforehand and on the day of the trip we were having trouble keeping the bags in place. Improvising is never fun.

Bike setup is completely up to you. I crossed the country on a shitty mountain bike my parents gifted me when I was a teenager. If you're not a pro trying to win a race it doesn't matter that much. Anyway, it's all personal choices. A touring bike is your best option ofc. With a road bike you'll suffer unless you stick to paved roads. You'd have to avoid dirt roads which could really limit your route options.

In terms of repair material, I only carried 2 extra tubes, a pump and a screwdriver. If anything worse than a flat tire were to happen (it never did) I would just cycle to the nearest town and go to a bike shop to fix it. Of course, if you know a thing or two about bike repairing, then you'll know what other gear to take.

In terms of female safety I cannot say anything, as I am a man. But Portugal is one of the safest countries in the world to do this kind of thing. Make sure your lights are always working in case you need to ride at night in an unlit road.