Backyard Rabbits

I would never put a rabbit out in the backyard with a cat flap like someone else recommended. There are way too many predators that would make a quick meal of your rabbit..
I keep my rabbit inside because we have too many predators around. They do prefer cooler weather, but, they are pretty adaptable at the same time. They definitely wouldn't like a hot summer day outside.
What I use is the largest dog crate I could find, they tend to be cheaper and MUCH larger then the cages sold for rabbits. All I do is use one of those corner litter pans with wood pellets in it ( like feline pine or pellets made for wood stoves so long as they don't have any kind of propellant in them to make them burn better) then I use aspen for the rest of the cage. However, my rabbit spends most of it's time outside of it's cage.
Initially, you'll want to keep your rabbit in the cage for the first couple days whenever you can't be around to watch it. That way you can make sure it's peeing in the litterbox. It will still poop everywhere, but, they're just hard little pellets that are easy to sweep up. Make sure to keep electrical cords out of reach along with anything else your rabbit may chew on. Some are bad chewers, but, my rabbit doesn't chew at all.
As far as whether to get a male or a female, I say get either, BUT get a neutered one. Males can start spraying as adults which is pretty gross, and some females get so moody they can hardly be handled.. You local shelter will probably be your best bet for that. It's a lot easier and cheaper to just adopt one that's already neutered. I always found the males to generally be friendlier, but, I currently have a female and she's sweet as can be.
No rabbit is truly hyper, but, Netherland Dwarfs are definitely one of the spunkier ones.. They're still more active at night like most rabbits, but, they'll get used to you being around during the day and will be more active after awhile.

Rabbits are pretty hardy so chances are it will be ok after it has some time to heal. Since it sounds like this is a feral rabbit I wouldn't worry too much. Putting out easy food and water is a good idea to give it a chance to heal without going to far from it's home, just don't feed it too close to it's den since that may attract predators.

That said I obviously haven't seen the rabbit myself. If you feel it needs medical help go to a tack/animal store (not a pet store) and get your hands on a rabbit trap (it won't hurt it, just keep it in one place so you can catch it and get it help. The trap should look like a wire cage with a door that will let the rabbit in then close on the end to keep them in (see link in source area for example).

Also, be careful what you put out for it… Leafy greens and veggies like carrots and celery are ok for rabbits, but you also don't want to over feed them on those kinds of things. Timothy hay and straw are good to provide as well (if it's possible). I have one bunny that ADORES fennel, cilantro and parsley and will eat himself sick on it if I give him too much.

If you're super worried I would google an animal control/rescue group in your area. They are the professionals in catching and treating wild animals that need help. Whatever you do I would NOT take it in like a pet and treat it in your home. Rabbits are capable of being very destructive and are MESSY as heck if you aren't set up for them.

I hope this helps. This is from my experience at work (I help care for a ton of rabbits and take them to parties and events for kids and adults to play and cuddle with without the fuss of long term care), so while I do have a goodly amount of experience I am not a vet. I hope your fluffy neighbor get to feeling 100% soon!

Housing guinea pigs with rabbits is really a bad idea as the rabbit could really hurt the guinea pig badly. It does not take much for a rabbit to get upset and kick and one swift kick and the game is over for the guinea pig. Yes when they are babies you will see them together in pet stores but only when they are all babies, and very young ones at that.Their dietary needs are so different also is a very serious issue and the guinea pig will come out on the short end of the stick with this combo.Also guinea pigs should not be left unattended outside as just as easy as the rabbit got into his area a cat could have or any of many predictor birds could have gotten to it.

I don't mean to sound like downer, i love guinea pigs to death, however they need closer watching and one and one attention then most pets.

Blessings and enjoy your guinea pig.