IMO the secret to rigid riding is a big fat front tyre, it just makes everything work better. For my 26er, that meant a singleply 2.5 Nevegal- light and sensibly fast rolling. I could do it with less tyre obviously but things were more fun with a bit of bounce.
I had 2 sets of carbon forks, some exotics with alu steerer, and some very light Hylix full carbons. The exotics were a bit heavier, cheaper and unexpectedly a lot flexier, they were quite funny to watch- hard braking was like drawing back on a bow. But that worked really well in use, it was like having a set of early Sids with more sideways travel than vertical. The Hylixes were way stiffer, which some folks would prefer I’m sure, they were also nicer looking.