I know of no set fast rules, several factors will determine the best approach. Material being cut, rigidity of set-up, width and depth of cut as well as style of the saw. As with an end mill a saw that will cut the depth and width you want should only be large enough in O.D. to cut to your depth and clear work, saw arbor, etc. In other words, if you only need a 2" saw, you don't want to use a 6" saw. The larger the saws get in diameter to width, they may deflect while cutting. I have made cuts up to 1/2" deep and .040" wide in aluminum, using a 3" saw, w/o incident. Use lubricant and keep cut as clear of chips as possible. Use a saw that has enough teeth to cut the work without "loading" the gullet, (softer materials), yet not so few that the teeth are "hammering" into the cut. Spindle speed and feed rate can be of help here.
Paying Attention Is Not That Expensive.