@questions about . . . . - you don't say what dimensions of barn you are considering. Or rather what dimensions you can afford to put up. Without those dimensions it is hard to advise you on what you can fit inside.
Overhangs can be installed for feeding. That way you can feed from your dry hay stockpile inside the barn and the animals can eat from outside while under cover. This is best because you won't have to let them into the barn to eat during nice weather. Remember that you will have to clean any animal areas so the less time they spend in the barn lined up at a feeder the better. They will pee and poop while eating so better to do it outside the barn where you can tractor or rake and shovel it away more easily. If you can plan an area for a compost pile where the poop and bedding can be dumped it will eventually break down into good garden compost. You will need to toss it to aerate it every week, but of you have a small garden tractor that should be easy.
Whatever you are planning - if possible, double the size. You are in Virginia where the humidity is bad so you will need some air circulation around your hay. In drier areas you might consider a large Connex container for hay storage. They work great in California but in Texas they don't. The climate of your area will determine what you need for hay storage and barn space. A covered barn with a large permanent covered loafing area for the goats in winter rain and snow is necessary (also gives a shady spot in summer). You will need confined areas for the does when kidding. Depending on whether you opt for doe raised or bottle raised kids, those areas can be used just to kid out the does before separating the kids into a kid pen and putting the doe into the milking herd, or to hold a doe and several kids together for several weeks. Movable panels to make kidding pens, and for holding bottle kids is good. The moveable panels give you more options in layout since your needs will change over time. You can make the panels yourself from wood, or wire on pipe. The panels can be bolted together, or wired together. Portable panels have the added benefit that they can be taken apart and stored when not in use.
Whatever you put up, make sure you have electricity and water. Lanterns are cute but flipping a switch is easier and provides better lighting. You will need a couple battery lanterns in case of power failures. Having a water source in the barn makes it easier to water the animals and for cleaning up. Milking and kidding can be messy. You don't want to have to run back to the house for a bucket of water in the middle of something. Since you will be milking your goats, you will need a covered area large enough for the stanchions with room to walk around them from side to side. You will be using them to trim hooves and to do some udder clipping depending on breed of goats.
We are in southern California. Our current barn is 24 x 36. It is recessed 4' below the grade of the driveway, the next level down is another 6', then another couple feet to the rear slope into the gully. We are on very steep ground. We built the barn with a loft where we stored sack feed and hay but had to remove it because the horizontal timbers began to crack from the weight. In that 24' x 36' barn we have an area 10' x 24' at the end. Since we no longer have dairy goats but White Dorper sheep now, this 24' wide area is divided with a creep panel to allow for a 10' x 10' creep pen for the lambs. The entire 10' x 24' opens out onto the rear hillside on the 10' end. 24' of the 36' is enclosed by the upper 4' of the 10' x 24' block building that at one time was used for a milk shed and hay storage. The other side and end of the barn is enclosed by a block retaining wall for the upper driveway. This was the only flat area on our property where a barn could be built when we moved here before we purchased the adjacent 4.5 acres.
This barn is too small. When we were milking dairy goats, the hay had to be dragged down into the "milk shed" to store, and carried up to the barn to be fed to the dairy does. We had 2 homemade double wooden stanchions set up at one end for milking. Towards the end of our dairy keeping we milked about 12-18 does am and pm year round by machine. We put 4 in the stanchions, the machine milked 2 at a time, and we stripped by hand. Across the path from the barn, we had an 8' x 12' wooden shed with a 30' x 20' yard for the young kids. They were fed with nipple buckets. Once they were about 4-6 months old they went in with the does. Since they were bottle/bucket fed from birth they did not nurse the dairy does. The barn was on one side of the house. We kept the bucks on the other side of the house.
Now we have only sheep so we store some hay in the barn where the milking area was. The main hay storage is in a 24' Connex storage container on the field. We can fit about 120+ bales in it, and 15-20 bales of 110 lb. alfalfa bales in the barn. In California we don't have any grazing except in the spring if we get heavy rain. Then we get weedy forage. We dry lot feed year-round. The 10' x 24' fenced area at the end of the barn is used for ewes and newborn lambs. We have portable panels which we set up for lambing pens during lambing in the main part of the barn. We don't have enough room to lamb the entire flock at once, so we breed all year round. When we wean the lambs, the ewes are removed and put back with the main flock on the field. We have several more fenced areas and temporary panel pens for rams and breeding flocks now that we have the extra 4.5 acres. Our property is fenced with 6'-7' wire on pipe.
When we move to Texas we have 6' wire fencing and a larger barn - 40' x 60'. It sounds large, but we will have to store some of our hay inside the barn. We won't be able to use a Connex storage container in Texas due to the heat and humidity. Although we have pastures and will do rotational grazing, the grass stops growing in the winter and we have to plan ahead and lay in enough hay. Most of the hay in round bales can sit outside if we are going to feed it that winter. Any other bales, and any alfalfa needs to be stacked and stored inside the barn. DH wants to put up a much larger open sided hay barn for hay storage and to park our vehicles in.
Remember when budgeting that you want to put up as large a barn as possible. Covered space is always valuable.