Quickest to Paddington is the LHR-Express, one every 15mins and 15min journey time. Taxi from station rank or bus/tube to your final destination.

If there are two or three of you then a Taxi might work out .. but the airport access fee is around 30GBP so the odds are stacked against you.

Tube take around 90mins depending upon were you want to go number of changes etc and can be very difficult if you have a lot of bags.

Bus will take about the same about of time (9pm ish) and there might be one which stops close to were you are staying. Downside lots of hanging around as the routes can be infrequent.

The best alternative is private limo hire, search around and you will find numbers of drivers willing meet you at arrivals and take you anywhere .. for a very good price (they avoid the access fee).