I noticed something in Clark's photo of the indexing head, that he did correctly, and should be pointed out. Always leave the quill or spindle up, and use the knee to raise the part when milling. I've seen many bring the quill down to meet the part, and an extended quill will cause chatter. Always, keep everything tight and drawn up as close as possible. Use the quill for drilling and tapping only, unless you have to reach inside a cavity, and if so, take lighter cuts. Always lock the quill when milling.
On lathes, you want to do the same thing, especially when parting.