I've got thousands of coins which have increased 100 fold or more. I'm not sure it was worth all the effort and time but it's been a lot of fun. Just figure out what's scarce and cheap and time will take care of everything else if you live long enough.
The OP asked "How should I handle modern 'investment coins' from the US Mint?" I handle almost all coins by the edge, but I think i would handle all modern investment coins from the US Mint by the front and back.
The Modern Mint Market can be very fickle. A lot of how well something does is not only he demand but the mintage of a product. Generally regular proof and mint sets don't really go up in value because of their large mintage. Special releases from the mint can be very profitable. An exam of this is the Truman Coin and Chronicles. They sell for multiples of initial releases price. That set had a very low mintage. The last two chronicles sets aren't as valuable and didn't have any upside due to their enlarged mintage. Usually eBay pre-sales, Mintage and performance of similar products will give you an idea of wither or not to invest in the product.