Chocolate ganache tastes the best for drips and is pretty easy to make. (White chocolate is a little more difficult to work with and I'll cover that in another post.
I used to use candy melts to do my drips, which work really well if you want colored drips or are just starting out to work with dripped cakes. They're very beginner friendly in that they're easy to melt and easy to drip onto the cake. They do, however, harden completely, like candy! So if you're decorating anything on top of the drips you have to work fast.
In my opinion, real chocolate tastes so much better and is not that much more difficult to work with.
A medium ganache that has been cooled slightly works great with buttercream cakes.
You are looking for a 1:1 ratio of heavy cream to chocolate.
I find that semi-sweet, dark, or bittersweet works best in terms of flavor. Since you will be diluting your chocolate with cream, milk chocolates tend to lose their chocolate flavor a bit. However, if you're a fan of milk chocolate, by all means it will work as well.
You can use chips, bars, or leftover chocolate from candies as long as it doesn't have any additions, like nuts and coconuts and that sort of thing. Just make sure you chop it up pretty well so that it will melt.