BCN to Hotel Jazz transportation

Best? Cheapest? Most convenient?
You could take the Aerobus to Placa Catalunya and walk about 2 blocks to your hotel. About 7 EUR per person.
You could take an official taxi direct to the hotel. About 40 to 50 EUR total.

I agree with the previous poster. "Best choice" is subjective.
In the past, I have used the aerobus from BCN to Plaça Catalunya and walked (i.e. wheeled my luggage) the 2-3 blocks to the Hotel Jazz. It's a nice hotel.

If there are two in your group, take either the A1 Airport Bus if your flight is arriving at Terminal 1 or the A2 Airport Bus from Terminal 2 if you’re arriving there. There are only two Airport terminals at BCN “El Prat”Airport.
Buses depart just outside the terminals every 5 minutes and stop at four locations in central Barcelona. The stop you want is the 4th and final stop— Placa Catalunya.
The Hotel Jazz is 400 meters from Placa Catalunya.
The bus ride takes about 35 minutes and costs €8.90 per person. So, if there are three in your group a taxi or Uber likely makes more sense.