For a group of 3, I'd get a taxi. The cost saving is greater than you think - Hex is now £16 if you buy the ticket on the train, and the tube is now £3 for a single - so 3 of you will spend £57!! The cab may even be cheaper.

From LGW, I would - for simplicity only - take the Gatwick Express to Victoria and then a cab. However, in practice, you can get the first train that arrives and get off at London Bridge if its a Thamelink and get a cab from there, or Victoria if its a Southern.

The advantages of the Gatwick Express are a) there is always one waiting on the platform so you can get on and sit down and b) you can buy the ticket on the train. These are both big pluses.