Hey i bought my rabbit about 3 months ago and have him as an indoor rabbit, in my local petshop they sell a decent enough starter kit which includes a hutch, water bottle, food bowl, hay bale and sawdust for �40. I started off with that and had him as an indoor rabbit but then changed to a cage as he is male he kept doing his business outside of his hutch through the mesh!!!probably marking his territory. Also cages are much much easier to clean! I wouldnt keep your bunny outside if cats are known to be about. What i do is take him out for a fus and give him the run of the kitchen and put his cage on the floor for him to go in and out of and luckily my bunny trained himself and hops in his cage to do his droppings then hops out again!
Id personally keep a rabbit as an indoor pet they tend to get a lot more attention idoors :)
Also another thing i didnt know from the start but do now, until your bunny is 6 months old only feed him on his food mix, hay and a small amount of veg (but no lettuce), you shouldnt really introduce lettuce or treats until they are 6 months when theyre stomachs are properly formed!