Quickest and most comfortable way from Heathrow to hotel is probably
to take Heathrow Express train to Paddington and taxi from there (may
be a queue for taxis at that time). Quite expensive though
particularly if there are several of you.

Cheapest way is probably to take Piccadilly Line tube to Hyde Park
Corner and walk to hotel from there (5-10 minutes). However the tube
will get increasingly crowded with commuters as you approach Central
London and the more luggage you have the more stressful will be your
journey.

If you travel by road you will also hit the morning rush hour and you
will probably be stuck in traffic for part of the time (although if
you take up Mr Hughes's offer he may be able to keep delays to a
minimum)


When travelling to Gatwick in the evening I recommend either walking
(15-20 mins) or getting a bus to Victoria and then taking a fast train
to Gatwick (fairly frequent). You could also return by train and get
a taxi from Victoria to the hotel.