Kids can be bottle fed from about 4days onwards, but it will be VERY expensive to raise them on milk replacer. Also you will need to vaccinate them very soon (about 4 weeks onwards). I wouldn't take them from the owner of the nanny (so that s/he bottlefeeds them) until they are about 12 weeks old, by which time they will be weaned. if you were to take in any male kids, make sure they are castrated (rubber ring before 7 days of age), and it would be up to you to have disbudded (to be done at 4 days) or keep their horns. If they stay with the nanny, the owner would organise that through their vet. I get all of mine disbudded, it's safer.
I would say you would be better off to buying a goatling (and friend - either another female or a castrated male) and get her into kid yourself, or buy an in-milk nanny with her kid(s) in the spring, then you have milk straight away.
Also goats are not lawn mowers - better to get some sheep for that job. You will also need a CPH number and get a goat herd number, although any you buy in will come with their own herd/individual number. Any goatlings or younger will need to be double-eartagged, but not EID.
Lots of info on the BGS website,
www.allgoats.org.uk