I save all my copper pennies, and all nickels which are iirc 75% copper and 25% nickel. I also save any scrap stuff I can find of whatever PM there is. My dad buys the copper coins, but to me the premium is just so crazy. You usually pay for an ozt what you nearly could get a pound at spot.
I do NOT give any representation for this company [either positive or negative] since I've never bought anything from them, but I'll post a link so you can look at what is out there for sale right now. Copper bullion is an interesting niche market right now, and prices have fallen quite a bit in the last ten months. I have a handful of one ounce rounds that I bought because I thought they were cool, and they are from the company I linked below, but bought from a third party at the gun show.
When I decided to get into PMs I looked at what I had already (some minor stuff) and recalled that I had bought two copper "coins" at a gun show last year. One oz coins for which I paid maybe $2 each. I could be wrong but it seems to me that this would be the biggest market for small amounts of copper, commemorative coins rather than the value of the metal.
Base metals can be had for less than spot if you are willing to cruise the alleys looking for scrap. I do it from time to time to remind Little Ancona that one is never "too good" to do a little bit of salvaging. In fact, we've hit the proverbial mother lode a time or two. Once, we got hold of six pick-up truck loads of 302 stainless tubing that was tossed out back of an OJ bottling company that had been sold and was being converted in to a Tractor Supply warehouse store, and another time we got hold of a bunch of dry type pad mounted transformers we sold to a broker in Orlando. Since then, she's all for the scavenger hunt. Sometimes we get the big goose egg, and sometimes we just barely cover gas, but on the whole, we do all right.
As for base metals, we do find our fair share of copper, stainless steel [good source of nickel] and other metals. Other than some finished metals for repairs and perhaps making things post-SHTF, I see little value in stockpiling much more than a small pile of base metal. I have several spools of various gauge copper wire, several rolls of romex cable and some comm wire, and also have sheet aluminum in the form of 36" flashing. We have a little bit of copper tube left from re-piping the house six or so years ago and most of a roll of dehydrated copper from re-installing our A/C several years back. Other than that, nada.