I have a few ideas as to your questions from what I have learnt in the past year.
The best cage depends on where your rabbit is living. Mine are outside.If they are outside the best idea is to have a wire bottom and wire onthe front of the cage, the rest should be wood so that they aresheltered from wind, rain, and snow. But remember, if they have a wirebottom, they need things to protect there feet from getting sores, wesimply use scrap wood that has no paint on it so they can rest therefeet and its easy to replace if it rots. Rabbits need places to hide,when they become scared, the like dark places. Mine have cardboardboxes with rabbit sized doors in them until my dad can build insulatedwinter wood boxes for them. We use straw for bedding in them so theyhave a place where its nice and soft.
If they are inside, a large cage should do (depending on the size ofrabbit you get). Never use pine or cedar shavings in the bottom, norclumping cat litter, use newspaper or newspaper cat litter. Most have awire grate on top so stuff falls through and your rabbit isn't sittingon wet stuff (some don't) but if they do you need to have a place theycan rest their feet.
Rabbits need out daily, even mine get out in the winter, they LOVE snowand I just make sure they are dry before I leave then in their cage forthe night. We have an outdoor run where they can dig and run and eatgrass, but watch out for digging, they can dig fast! If they areindoors, make sure the wires are protected or well out of reach.
Depending on the personality of the rabbit will depend on how you playwith them. Some you can't really play with them as such as they playalone but you can pet them for hours (they love it). Some rabbits willplay fetch but I don't know if you can train them to do this, it mayjust be a natural thing for some. Spice absolutely loves to chew, heeats toilet paper rolls, shreds newspaper, eats his cardboard house,eats plastic fruit containers. The best thing for these guys are piecesof apple trees, they love the bark! (if you know someone with an appletree it's cheaper to get them to cut off a branch then to buy chewsticks) Mocha on the other hand, loves to thro things, he normallyplays with toilet paper rolls, small sticks, and fruit baskets. Makesure they have wood for there teeth as it keeps their teeth healthy andfrom growing too long.