I go West Hampsted (overground) West Brompton (District, 1 stop) - Earl's Court (Picadilly) Heathrow. Swipe the Pink card reader @ West Brompton to ensure the non-Zone 1 fare (easy across platform change here too)

You can also change at Gunnersbury then Turnham Green (and Acton Town). That's normally slower due to the extra change, unless you need to be at LHR for around 7.30am, when the Picadilly line still stops at Turnham Green. In that case it's actually the fastest way to Heathrow (well, faster than the tube anyway).

The only problem with the Overground is that it doesn't run as often (sometimes off peak there's a 20-30 min wait), and doesn't run very early or late. I use it far more often going to LHR as I can time my departure from home. Coming back, it's probably 50:50 with the tube, and I decide when I'm on the tube already and approaching Earl's Court. If there's no good connection, I stay on til Green Park then change onto to Jubilee Line.

One major benefit of the Overground route is that it's above ground (duh!) pretty much the entire way, which is generally more pleasant, and tends to be less busy than the tube. And on those rare hot days, it's air con!

From Highgate isn't not as simple/time effective. You would have to walk between Camden Town tube and Camden Road Overgound....I'm still not sure if "overland sectors" count as a connection....I've only experimented at Kings Cross going from Tube to National Rail where I was charged a weird half fare...YMMV. Give it a go one day when you're not in a rush (although it will probably be much more time consuming than just a one change at Kings X.

I think from West Hampsted it's a bit of a sweet spot as the timings work out, and the tube station is next to the Overground, so they are both as convenient as wach other.