Flight
This is the airport we recommend, because it is the bigger airport that offers more airlines and cheaper flights.
Train
This is the train we recommend to take from Paddington to Penzance (from there you can rent a car). They offer sleeper trains, where you can take it overnight to arrive in the morning. They also offer day trips, if you want to do some sight seeing.
Rental Car
If the train doesn't suit your fancy, you can rent a car by the airport. You can choose anyone to rent from but, everyone knows Budget. Disclaimer! This is Europe and the cars drive on the left side of the road! That being said we recommend taking public transportation as much as possible.