yep, "alpine" would be your goat breed...
there is definitely taste difference in the goat breeds' milk as well... we have a bunch of LaManchas and a Kinder, LOVE the milk from both, mild flavored (not goaty) and rich. I *don't* like toggenburg goat milk, it tastes goatier to me, however if I was making some kinds of goat cheese it would be a more appropriate choice to get the "goat cheese" flavor. I've made goat mozzerella from my goat's milk and it tases exACTly like commercial cow's milk mozzerella... if I want a "goat" flavor I have to add stuff to the milk to create it.
there are a LOT of things that can affect the milk taste... breed, diet, how the milk was handled, health of the animal, where in the lactation cycle the animal is (milk content changes the longer they've been in milk). there's a popular theory that keeping a goat buck where the does can smell him changes the taste of the milk (the buck musk makes the does make muskier milk) but in my own experience I haven't found that to be true (conducted the experiment). Bucks do stink during rut season, and if not properly handled, I can see milk picking up the scent of whatever's in it's environment... but the buck-nearby theory didn't hold in our case.
I can only recall "metalic" milk once, and that was drinking fresh milk out of a steel cup, one where you could smell the steel (not unpleasant, but definitely present). don't know if the milk actually tasted like steel, or if it was just my nose picking up the scent while I was drinking the milk, but I can imagine the milk might pick up some of the scent.
I do know that galvanized metals (like many buckets) can give a metalic taste to milk (the tin and zinc do it)... if enamel equipment is used, and there's a break or chip in the enamel, the underlying metal can affect the milk. if stainless steel is used, but it's stainless-over-something-else and the stainless is cracked or damaged, or has been repaired, there might be contamination from that as well.
BTW, the metals coming off a galvanized container can be toxic, although probably not in tiny quantities.
I did a little searching on-line and I found some sources for the following info on what can cause a metalic / off / ricey / soapy / chemical / band-aid / medicinal / skunky / old cooking oil / <many other descriptions> taste in milk (see below). interestingly it's getting anecdotally reported in high percentages (relative to amount of milk sold) for organic products - I think that may have to do with the different rules in feeds for organic milk cows vs. factory-farm cows. here's some of what I found, a variety of these things might apply to the raw milk you purchased.
1) wild onions in the feed (more common than it used to be because of changes in regs about herbicide use)
2) ethanol in the feed (comes from fermentation of feed, either because it has gotten wet or excessive fermentation of silage feed)
3) oxidation of fats (from not cooling milk fast enough, exposure to light in see-through containers especially when stored in lighted dairy displays, exposure of the milk to air during processing, over-aggitation of the milk during handling, also agrivated by ultra-pasturizing process' higher temps)
4) other contamination (cleaning chemicals, improper metals, HDPE from the plastic containers, dust or contaminants from the animals or handling... lots of speculation here)
5) change in regs extending the "use by" date for milk, so milk may be older and less fresh
6) The distinctive medicinal/bandage/band-aid smell is caused by chlorophenols (cleaning agent used in milk processing equipment, cow foot-baths, etc.)
7) soapy taste may be oxidization (fats break down into aldehydes- which are part of what's in soap)
8) soapy-bitter may be rancid from bacterial breakdown of the fat (improper cooling and handling)
the dairy industry defines them this way:
Absorbed – feedy, barny, cowy, unclean, weedy, and musty. (caused by improper handling)
Bacterial – acid, malty, unclean, fruity, and putrid. (caused by improper handling)
Chemical – cowy (ketosis), rancid, oxidized, sunlight, and medicinal. (caused by contamination, medications, improper handling)