Have once stayed at Vertice. It's in Sevilla Este and about 7 kms from the old city area. If you want to take a bus then the airport bus will take you into Seville via the Avenida de Kansas City and will finish next to a park : Prado de San Sebastian. (the final stop) you would need to walk around the corner of the park towards the north and where the tram is and look for the stop on CARLOS V AVENIDA (park is still next to you) for bus Route 22. Prado - Seville Este. This bus will go past the Seville football stadium reaching the main route east out of Seville called Avenida Andalucia and fly down this wide road until it turns off into Avenida de la Aeronautica where the Vertice is on the left side across the road. You should be able to see the hotel once you finally turn off the main road or ask the driver. the stop should come up on the indicator board : LA AERONAUTICA (Helios) or something like that. It's a fairly easy and frequent bus journey.
You can look up more info on TUSSAM.
I suggested going right to the end of the bus route from the airport although once you know the ropes, you can change buses on Avenida de San Francisco Javier which may save you some minutes. Cross over this road to take the 22.
Don't know what you mean about Ryanair. Depends if you are travelling light with cabin bag or not I suppose. You must read through all the T&C on the web site to fully understand all. Ryanair now has a 'hub' at Seville airport so promises to provide a larger service and so far have found them excellent. I think best advice is to read the terms and follow these and you won't go wrong. Ryanair has a desk at Seville airport for problem solving in case you need it.
Taxis do charge for 'waiting time' at the airport and you will probably be charged anything around €20. the taxis are metered just depends on the quickest route they take etc etc.
Airport bus costs €2.30 and the fare on the 22 is €1.20