Haven't booked flight as yet but thinking of flying from U.S. via TAP Portugal to Gatwick Airport. From that airport, looking at possibly staying at a BnB in New Forest (Lyndhurst). Transportation to get from point A (airport) to point B (BnB). What is the best way to go or should I continue looking at other places to stay? We plan to stay for a few days in the area but want to go into London one day and possibly to Windsor before heading to the port in Southampton. Please advise. Thank you.
From Gatwick, you need to take a train to Clapham Junction (towards London), then change and take a train to Brockenhurst. From there, it's a bus or taxi to Lyndhurst.
There aren't many fast trains from Clapham Junction to Brockenhurst. I think a more convenient route would be to take the train from Gatwick to Southampton, and change there for Brockenhurst.
There is only one train an hour direct from Gatwick to Southampton, although more if you change once or twice, which is riskier. At most times of day, going via Clapham will be 30 minutes quicker.