There are probably millions of different possible placements for overhead microphones. There are many different schools of thought ranging from X-Y, to stereo pair, to cymbal wash. Each of these has a different idea to it, and I can’t tell you which is the best for your set. I can tell you how to go about thinking of these three schools of thought.
For X-Y, what I have found, is the best way to do this is to put the X-Y pair above the head of the drummer facing the low-cymbals/drums line. Meaning that I aim them at the edge of the cymbals and get mainly cymbal wash, and a bit of the drums. The important thing is to get them about 3 feet from the snare. This is roughly, where I have found, the easiest distance to find if there is a phase shift needed. Listen to your own overheads and snare with phase shift on and off and determine which is better for your mix.
For a stereo pair I like the idea of 1:3 feet. For every 1 foot up, 3 feet apart. I tend to do 2 feet above the kit, and 6 feet apart spaced evenly across the center of the kit. This tends to give us a good stereo sound. Again this gives us about 3 feet from the snare, and gives us the ability to phase shift if we wish. Remember there is no rule that you have to have stereo overheads.
Overheads can be used strictly for the cymbal wash. This I tend to use the same rule of 1:3 as I use for stereo pairs, but I bring them up to the cymbal line, instead of centering them around the kit.
There are many other ways to use overheads, and I cannot get them all in this chapter, and no matter how many I state (though I think these three groups cover many of them) there are more that I cannot. Do not be scared to experiment with overheads, and the placement of them.
As for microphone choice, I would go with a for live settings almost always. For the budget option the Behringer C-2s are surprisingly decent for a sub $100 USD option. I would recommend either the Audix ADX51s or the Shure SM81s coming in between $500-700 USD. The top of the line for a live setting would probably be the Telefunken M60 FET at about $1500 USD. It is very easy to loose a lot of money with microphones. I used a set of SM81s for this book.
A type of condenser microphone that is long and skinny, a shape similar to a pencil. They are also called Small Diaphragm Condensers.