Again, don't panic. Unless you show your goat you can take your time to get her feet better trimmed, and I wouldn't worry too much if they are a bit overgrown - as long as it doesn't cause her discomfort or she starts to stretch her pasterns by standing on her heel.
Get her feet damp - wet grass, or better give her a bath (on a warm day), and make a first start on her feet then - they should be quite soft then and any dried mud/muck etc comes away easily helping you see where to cut. Also maybe have someone helping you. Goat needs to be rugged with an extra towel under her coat and preferably stabled until completely dry.
I fine the smaller lamb size footclippers better in my hand. And yes a little at a time will do. She may well object to the pedicure if she is not used to it...
If she has any other problems - like lice, worms etc - I would deal with them first.