Best mode of transportation in Spain around Barcelona

I was wondering what I should use to travel around Barcelona? I’m gonna be there for a week and we want to be able to go around and such. We were also thinking to going to Madrid for a day and catch an early train there. But before all that, I was wondering what I should use to get from the Barcelona Airport to my hotel. My hotel is about 5 miles away from the airport and we are 2 people traveling. Our luggages are that big, we can definitely hold onto them when in a bus or train. Are there any apps you recommend I should download? Thank you!