Unless you are seriously into pedigree breeding I wouldn't undertake AI in either sheep or goats. If you do - laprascopic is best but needs to be done at special vets/AI centres (such as AB Europe). If you only want sheep for meat, then byuing a few Shetland lambs at weaning (wethers are best), having them on grass and hay over winter (no shed needed for them) and then get to the abattoir at 18 to 20 months old - wonderful meat, but you do need to shear them in the spring. Meat gets even better after 2 to 3 years old. No need for hard feed at all.
As to goats - AI difficult and you would be struggling to buy semen unless you are a BGS member. You can often take your goats to a nearby male for mating, but would need to be whole-herd CAE tested at the minimum. Goat and sheep semen needs to be stored in liquid Nitrogen tanks, so unless you buy your own you need to store any semen with one of the companies offering AI.
Goats are expensive to keep well (hay and hard feed all year round, plus stable/shelter), and keeping a male for a small number of females is also expensive (separate housing, plus he needs a wethered companion too). Goats do take up much more time on a day to day basis, especially if you are milking them. You will need a trailer (and car to tow it) for taking females to the male, and to the vets etc.