Snaps and thickness!! Snap bibs are essential as velcro bibs will ruin your kids' clothes when you put them through the wash. These bibs really last. The thickness of both the bib and burp cloth hold up nicely and will prevent their shirts (and yours!) from getting wet.
Some other brands we love: Diaper Squad Bibs and Green Sprouts Burp Cloths. Don't skimp on burp cloths! If you have a happy spitter or a baby with reflux, you'll need the thicker ones and lots of them.