this my method
First off, a proper rode length will help the anchor set without having to really bury it by backing it down. General recommendation is a 7 to 1 scope (length of rode) to depth ratio and at least as much chain as the boat is long. Having gotten that out of the way, it's huge overkill when you're just anchoring for lunch! If I were overnighting and wanted to actually sleep well, I'll be using 7 to 1. For a casual anchor, I find 3 to 1 to be sufficient, and I rarely drag. Also anchoring in a muddy or sandy bottom is best for setting and avoiding snags when retrieving.
My retrieval method works pretty well, and I haven't lost an anchor since I got this boat 2 years ago, and for a while before that with other boats. I bring in the rode by hand and keep it wrapped around a cleat. When I reach the point where it starts trying to play out again (which is when you are over the anchor) I cleat it off and wait a few seconds. 10 or so. Then try to snug it up again and much as I can and cleat it off again. Repeat a few times and it will pop free. What you are doing is using the boat's bobbing in the water to pull the anchor straight up. If you are not hung on something, it WILL come free. You just have to be patient.
I have also heard good things about box anchors.