Eventually you'll find that the better approach is to learn compounds rather than single character/single readings. However, you need a base from which to start.
There isn't a single source I know of, but what I did was use a made for Japanese schoolchildren kanji dictionary of the first 1006 elementary school kanji. Mine was a Doraemon one which was a bit embarrassing to carry around, but there are a few different ones. For each character there will also be compounds using that character. Looking at the readings for the compounds you can see which on reading is the most common, with reasonable confidence.
Alternatively, use a site like
http://jisho.org/kanji/ and input the kanji in question. Then chose from the "words beginning with" and "words ending with" links and scan which reading appears most. (Also, on the results page there's a checkbox to restrict the results to "common words only".) This should also help figuring out which kun reading is most common.