Help with Itinerary: one week in Budapest and Transylvania

Hi guys. I need some help with an itinerary. I will be in Poland for a couple weeks in June for school. I'm Romanian, and since I'll be so close I'm going to stay a week later to visit Romania. I'm mostly interested in seeing Transylvania. I also saw Budapest is in between Poland and Romania so that I might also add 1 or 2 days there.

I will end my trip in Poland in Krakow. Should I just fly to Romania from there or take a train to Budapest, spend a couple days, and then take a train to a Transylvanian city. Also how do you get around in Romania. Is public transport good? I don't want to rent a car.

The cities in Romania I want to see are Brasov, Sighisoara, and Sibiu. Are these good or what would you recommend to see if I spend a week in Romania?

Thank you