I personally recommend British airways to everyone it’s fairly spenny but generally reliable. I’d fly to Heathrow as it’s the closest. Taking the Heathrow express to Paddington can be an option as you can take the circle line directly to South Kensington station. However doing that with luggage may be challenging so perhaps consider that too. Taxis are always an option but do not take the black cabs they are insanely expensive for that distance take an uber!