RE: what herbicide to use?
2-4D Amineand 2-4D LV will both kill clover. Can't remember which is which, but one has 65% active ingredient (costs more) and the other is 46% active ingredient.
Clover is a bit harder to kill with 2-4D than other broadleaf weeds. The fine hairs on the clover leaf surface cause the spray to bead and roll off the leaf. It helps to add a surficant (dish soap) to reduce surface tension and coat the leaf.
There are some specialty sprays for clover/alfalfas, poast, select, arrest, and others. Some target grasses, other target broadleaf weeds, and they are a bit expensive.
For the best "weed free as possible" clover plot try a fall planting after three sprayings of roundup (glyphosate) the summer before. Also add 50 lbs/acre winter wheat and/or oats as a cover crop with the clover.