As the crow flies Heathrow is closest, although you may want to look into flying into Southampton if it is possible.
Unless you are going to rent a car at Heathrow it might be a lot easier to get to Farnborough from Soton since there is a direct train link rather than either trekking into Central London to get to Waterloo or braving the Heathrow-Woking coach link.
Edit to Add:
Gatwick may also work better for you as well since there is a rail link that will easily allow you to go Gatwick-North Farnborough/North Camp station