I've kept dairy goats in a few different ways.
My experience with portable electric chicken netting was that some goats respected it, and some didn't. Saanens were more likely to respect it than the Toggenburgs and Saanen/Nubian crosses were.
Right now I do complete free-ranging as I don't have any goat-proof fences (other than one that I built to keep all animals out of my garden and orchard). Goats respond to this quite well, they are intelligent creatures and recognise the times of day when I give them food, or will come when they're called, so it's easy to round them up for milking. This is probably not the most effective method for getting rid of blackberries and other overgrown areas, as the goats tend to just nibble plants here and there. A combination of this, plus tethering some goats right next to the blackberries (or using portable electric fence) might work, but if you need to keep your goats out of the neighbour's land, then you'll probably need to get better boundary fencing.
I've also kept goats close to the house, in a strawyard, which is good for getting manure for the garden, but more labour intensive as you need to bring their food to them, and you don't get their blackberry-clearing benefits.
For land-clearing purposes, it's not so much the amount of goats that you have, but the concentration of them in a certain area with portable fences or tethers. Some goats have different plant preferences to other goats, so having more of them helps make sure that they're eating all the weeds, but around 5 to 7 of them should be enough for this.
My border collie/husky cross tries to herd my goats. It satisfies her instincts, and she's not rough with them, they don't seem to mind. I'm not sure how OES would go, it probably depends on the individual personality of the dog, so best to just observe and see how she is - if you know anyone locally that has goats you could always bring the dog there and observe, or see how your dog behaves around sheep.
Other things to know... Goats are more sensitive to soil nutrient deficiencies than cattle, so it would be worth looking at local soil conditions, and seeing if it is a bit too acid or alkaline, and if there's any minerals missing, if there are, then you can offer the minerals free-choice, or mix small amounts into their treat feed (my book '
Backyard Dairy Goats', and Pat Coleby's book 'Natural Goat Care', both have information about goat mineral requirements). Goats like their grass to be quite high - they prefer not to eat anything less than 6 inches from the ground. They are very selective as their natural instinct to avoid parasites, and many people that complain about goats being parasite-prone are often expecting their goats to be lawnmowers and leaving them on the same pasture for too long, or are moving them on to pasture before it's high enough (or aren't paying attention to mineral requirements).