I really like cheese. However, "goaty" cheeses are just not my cup of tea. I don't mind more mild-flavored goat cheeses, and I do like cow milk cheeses. I also like all different textures, from the soft to the hard.
The "What's your favorite cheese?" thread has inspired me to ask: What's your favorite cheese that isn't super-goaty (or "barnyardy")? I would like to try some new cheeses, but find myself shying away because I'm afraid they'll be too strong for my taste.
Go to a store/shop with a good cheese department, that has personnel. They will guide you and give you samples!
And check out _Murray's Cheese handbook_ Excellent guide. I am checking off cheeses I have sampled/tried as I do my bird Handbook for birds seen!
Try a Dutch goat gouda. I don't like goat cheese in general, except for this one. It's especially yummy when melted.
Is there a particular reason why you want to stick to goat milk cheeses? Cows Milk and sheep are also good.
hard to recommend a place to start, without knowing a bit more of what you like.
I would say to try to keep it milder as you explore, look for cheeses that are more mellowed, rather than aged. Look for washed rine cheese, not so much for ones with "bloomy" surfaces.