We raise California rabbits.
I have also had checkered and flemish and New Zealands in the past.
And I can say that I have never had any rabbit that enjoys being held, it scares them, it is akin to their nemisis the owl or hawk picking them up off the ground freaks them out.
My bucks are very personable, to the point where we have a halter for them and take him on walks.
They are big, though, and would be nothing you would want to pet or hold, he is nasty as a billy goat, cute though.
Rabbits can also rip you up with their claws ! Be careful !
To have and to hold ?
I highly recommend the lowly but wonderful world of cavies !
They are clean, sweet, have babies born on the run complete with fur and eyes open, and squeal with delight when you turn the doorknob and come home, or open the refrig as they expect a lettuce treat.
I adore these little critters !
Get a Guinea Pig !