My fixed wheel road bike. Steel springy frame, one gear ratio, no frewheel. Brakes. Every time I ride it I feel connected in a way that no other bike does. It’s just a wonderful ride.
Of course track is up there too, but a velodrome is needed.
Off road, it’s a rigid singlespeed. For largely the same reasons.
I would say track bike too. And no you don’t need a track. I road a track bike on road and off road for 10 years (as my only bike), last 5 with no brakes for extra ‘purity’
Gone soft as I reach 50 and now use a rigid single speed MTB but still very tempted to swap back to a track bike.