I'd say if you have the option, keep it inside. Bunnies are hilarious and fun to be around. I wouldn't want to miss a second with my bunner outside.
People have had a lot of luck with exercise pens for dogs, NIC cages & dog crates for indoor bunnies.
I personally think pet store cages are unacceptable, most are just a glorified litter box with a door.
People use all kinds of different beddings, anything from wood pellets, to blankets. Rabbits can be litter trained, that might be a good option for you if you use something like an exercise pen.
Here's a few set ups I've had:
Current, you can't see it well because I was trying to show how I attach the xpen to it, and also his fancy sheet. But that's the general size.
Cagecage
Older:
cagg
Oldest:
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The reason the last one is smaller than the oldest is because the cats kept jumping in it(which was fine before. They're friendly) but they started using his litter box, and I don't want that.. so I had to use a big piece of wood for the top.
Now he's in my bedroom, so no issues with needing a top.
Just for you, I took and uploaded a current pic of his cage. Ignore the poops,
IMG_1958