Bramble was a few days short of six weeks when I got him home (thats too young by the way but it was vet approved and circumstances at his parents house left little other choice) so I have experience with a baby bun. In my opinion the two biggest differences between a baby bun and an adult are that babies will often let you hold them whereas most adults dont like to be held and diet. A babies diet is unlimited pellets designed for young buns along with unlimited hay (alfalfa is fine for babies, but should be gradually changed as they get older) no veggies for a baby.
Baby bunnies in particular are very inquisitive, although adults are too. They will try and bite things (and unfortunately sometimes people) in an effort to find out what they are so bunny proofing is a must. I admit that I have never trusted Bramble around cables, no matter what they are covered with but I know others here have ways of covering them so they may be able to advise you on that. I personally block Bramble’s access to cables rather than cover them up.
I also highly recommend an x-pen, the one I have there is absolutely no way a cat could get in if it was covered on top and you can get nets for them. Try searching ‘rabbit playpen’ rather than x-pen on amazon, the one I have is massive and it wasnt expensive. I actually wouldn’t put a bunny outside at all, but I know others have a different opinion on this.
When your bun comes home, let him/her sit quietly in his/her cage/pen at least for the first day till they get at least a little used to their new environment, this helps with litter training too as they need to pick a place to ‘go’. Then you can start bonding with your bun, you will get lots of support here on that as we have all been through the process of bonding with a bun, be it a baby or an adult.
I just want to finish by offering a word of caution based on my previous experience with dogs and buns. I am not for one second saying that buns and dogs cannot live together because I know of several people who have both co-habiting quite happily. However you need to introduce them very carefully, rabbits are prey to dogs and they are also very sensitive. A friend of mine came to my door with his dog when i was a teenager, we had a wooden door and I didnt see the dog and opened the door without thinking, the dog ran into my room and my poor bunny died of fright – the dog had not actually touched the bunny at all he just died of shock. I am not telling you that to scare you, just to emphasise the importance of a slow introduction. Another rabbit I had got on reasonably well with another dog that used to visit our house regularly, although i admit i would never have left them alone.
I feel like I have talked more than enough (sorry) but if you have questions feel free to direct them to me and I will do my best to answer them, I am by no means an expert but I have been through it. Baby bunnies bring so much joy.