We've got a fantastic house rabbit, but I wouldn't recommend it.
Speedy MacReadie came to us as his second rescue home, as we'd had rabbits in the past. He needed lots of settling in about 14 months ago, and he formed a very strong bond with dd1, who is now 13. So strong that he learned to climb up to her loft bed (coming down didn't work so well!).
He's free range in the house, has a litter try he (mainly) uses, can go through the (newly installed, for him) cat flap into a safe, fully enclosed garden.
We don't pick him up unless he's happy (no chasing or scrabbling for him) and he often voluntarily sleeps on our bed in the sun (dd1 keeps her door shut but he still adores her, sleeps in front of her door at night!).
We have girl guinea pigs - they're never in with him, he's so much bigger, but he likes to lie beside their run in the garden.
I must impress : this is a very unusual rabbit. Especially as a 2x rescue. Most of it is down to him being so madly in love with dd1!
Guinea pigs are fab, but do get a pair (we actually have 6, 3x sibling pairs). My ds is 11 and is devoted to his piggie-girl. They love cuddles, they talk to you, they can be well tamed to not hiding - though I love our Speedy rabbit, my heart truly belongs to the Guinea pigs (my lovely big girls Sosua and Cabarete) who I was surprised with on Mothers Day in 2011!