Hi, I had an angora (years, and years ago), now I have cashmere goats. Yes, you do have to keep certain areas trimmed to promote good health in your goats, you don't want the dirty areas to persist, it can get pretty nasty. Go ahead and cut all that away, it's not good fiber anyway. Put your clippings in areas were the birds can pick at it for nesting material, (like the "crook" of a tree) they'll love it. Before you shear, whether hand or clipper, go ahead and clip all the extra dirty areas, then try to pick out as much vm as possible, you can use a blower (I used a compressor hose with the air sprayer thingy), some vacuums have a blower that may be powerfuly enough. Be gentle with the fiber. You will probably need help, unless they are very tame goats. I laid out a plastic tarp and had a helper hold the goat will I sheared. They will jump at first, but, soon they learn it feels so good they will stand for it. Keep your fiber picked up as you go, seperate the good from the not so good as you go. I've heard people say to shear with the lay of the coat, not against it. Harder then it sounds. And be sure to leave an inch or so on the goat, so they don't get sun burned while it grows back.
In the future, remember that your fiber is going to be as clean as your pasture, so keeping the "nasties" out of the fields will promote cleaner fiber. Makes the job alot easier next year.
Congrats on the new additions, hope you get more info, it's been awhile, but generally speaking what works for one fiber goat works for most.
Oh, watch out for "second" cuts, cut once, gather up the wool, then if you need to "pretty" them up, do some more trimming. You don't want those second cut short fiber in your fleece. Good luck!