If you can afford it, spray foam (closed cell) is the best. It closes all gaps, is a vapor barrier, and has higher r value. It costs an arm and a leg, and also can be applied sloppily. Open cell is cheaper but doesn't justify its cost.
For a diy, the most important thing to keep in mind is stopping the movement of air. Air disturbs the insulating quality and brings in moisture that may get trapped in the wall cavity.
(Air can dry out the materials, too, but it is better to compromise on the side of dead air movement and making sure there is no bulk moist vapor/water moving in. Rain and leak/condensation in the plumbing.)
Blown in cellulose is not really diy. Cellulose will settle in the wall, so it needs an experienced hand that can feel for the pressures in the hose for enough fibers in the wall that compensates for the settlement.
Fiberglass is only diy material in realistic sense. But it does nothing for the air movement. Stuffing it in is self defeating since you lose the r value. Since I am diy, what I do is this. I look at each stud bay and how the bay connects to ceiling and floor bays. Usually there are ceiling and floor plates that act as air barrier. But all lumber contact points, holes, cracks in lumber, etc, are open doors for the air movement. I use either cheaper caulk (Dap contractor pack) or spray can foam to close all joints in a given stud bay. I press in caulk along the sheathing joints. Then install fiberglass, vapor barrier and seal all opening in the sheetrock. In older houses with board sheathing, I'd use a sheet of 1/2 closed cell panel and seal the joint with spray can foam, then put in fiberglass.