I have two gorgeous crossbred pygmy goats, Teddy and Tumnus. They live in a pen 30 feet by 15 feet, built from stake and pale fencing covered with thick cattle mesh. Sturdy fencing is a must, chicken wire will not suffice, and it needs to be high enough that they cannot get their front feet over and bent at the knee. I have a purpose built goat shed which is 8ft by 6ft and has a fitted hay rack. There is also a low bench in there as goats like to sleep off the floor. I use wood chipping as a substrate and will add blankets in the winter. I have tried straw and hay as bedding but they eat every last scrap!
Goats are pretty weather hardy....can tolerate heat and cold very well and will grow/shed their fur accordingly. As long as their house is away from draughts, they will tolerate low temps well and they will need shade for hot weather.
I take them out for walks on a leash most days to give them more space, exercise and opportunity to browse. Their daily staple diet consists of free fed hay, a proprietry goat vitamin supplement (Caprivite) added to a handful of goat muesli and a handful of BOSS. They also have a salt and mineral lick in their house which they pay occasional attention to.
On their walks, they get to browse on a whole variety of trees....birch, beech, rowan, oak (best to stick to old growth), willow, apple, elm, hawthorn, as well as brambles, grass (usually only very long or dry), dead nettle and dandelion.
Any fruit tree that has pitted fruit, such as cherry or plum, are toxic and should be avoided. Any plant that grows from a bulb is also toxic (daffodil, crocus, tulip etc)
My boys will eat apple, pear, carrot, broccoli, spinach, sweetcorn, bread and water biscuits but these are rare treats, given in small doses because of the sugar/starch content.
They will also eat carrier bags, clothes, plastic storage boxes, chicken food (feeder and all!), chicken feathers, wellington boots, their leashes and just about any other seemingly non-edible item that you can think of!! I have found that goats can actually be extremely fussy over what 'real' food they will eat but will eat anything at all if it is something they SHOULDN'T have!
A fresh, clean water supply is essential at all times. In winter, it should be warmed as very cold water can give them stomach ache and in summer, a fresh, cool supply a couple of times a day won't go amiss.
My two boys are like dogs....they follow me everywhere, love to be petted, wag their tails when they're happy and also love playing with their football, chasing each other round, playing 'King of the Castle' and growling at each other when they've decided enough is enough.
Mine are both disbudded wethers. It is recommended that horned and de-horned/polled goats are not housed together as the horned ones will have a dominance advantage over those without horns but I have also heard of many people who have both together without problems.
Teddy and Tumnus get on fine with my chickens most of the time but have occasionally head-butted them to get them out of the way of a tasty bit of grass or whatever. They WILL eat all the chicken food so if you plan to co-habit them, you will need to keep the chicken food in a place that is inaccessible to the goats otherwise they will most certainly get fat while your chickens get skinny and too much processed food will also lead to potentially fatal bloat!
I have only had experience with pygmies at the moment....mine are about the size of a cocker spaniel and a springer spaniel I guess...but I hope to get some Nubians or Boers when I move to bigger premises.
I hope this helps but if you have any questions, fire away
By the way, you said you are getting about one egg a day from your chickens....do you mean one in total or one per bird?
Depending on their breed, they will settle down to laying one egg each per day/every other day but it may take several weeks after they first start laying, to get into this. They will not lay more than one each per day ever. The pure breeds tend to lay less than the hybrids and laying can be disrupted by poor health, new additions, broodiness, flock disputes, predator presence....pretty much anything that upsets them really.