Everyone uses their own technique, so it is best to listen to opinions, then to develop what works for you!
Our goat kids never suckle their mothers. They are bottle fed from the first feed, for two to three weeks. On their first day, they'll get 5 feeds, 4-5 fluid ounces to begin with, increasing to maybe 7-8 ounces for the last two feeds of that day. From day 2 allow 8-10 ounces per feed, but we only give four feeds. We give first feed at 6am, then 12 noon, 4:30pm, and before you go to bed- ideally 11pm so they only have seven hours with no milk.
Then increase the amount of milk gradually. Once they are taking between 15- 20 ounces (1pint) at a feed, when they are 2-3 weeks old, we move them onto drinking from a pan or bucket. They drop to 3 feeds a day, offering 35 ounces to begin with, though they don't take it all straightaway. Once they are established on the pan, depending how much we have they get between 1.5 and 2.5 pints at each feed. You may not want to give quite as much as 2.5 pints, 1.5 is adequate to be honest.
I would give them whole goats milk for the first 10 days if possible, then gradually start introducing the artificial milk ( you can mix real milk and artificial together, in different strengths).
Hopefully that helps, feeding on a bucket with teats may be a good option for you.
Beth