As with the other parts of our 2500-km road trip around Portugal, the little Fiat Punto rental car served us well. By this 5th day of the road trip, we had put about 1350 km on it without any problems at all. You certainly would not want anything much bigger considering the width of some of the secondary roads that we enjoyed taking.
Being a somewhat small city, it is easily discovered if you walk around. I thing it is the best way, as its streets are narrow and driving around may become a little complicated, at least for longer cars. Parking is not that easy and if you are walking around you won't have to worry about this and may wonder around at ease.
There are daily trains from Lisbon to Covilhã, as well as from other cities around the country. The train station is close to city centre and there are taxis and buses that may take visitors from train station to other places around the city or nearby localities. For further info on trains, check the Portuguese railways: www.cp.pt.
A good and comfortable to arrive in Covilhã is by car. This city is less than 300km from Lisbon, and most of the road it is highway, so the trip will be very fast and simple. A toll is required, but I don't remember value.