Our toilets do not flush very well. Meaning that it may take 2 or more
flushes to really flush the ****. The tanks properly fill and properly
release water, but it seems as though there is just not enough of
water to do the job right.

Obvious jokes aside, are there any toilets that flush very well (other
than commercial style toilets that seem to have vacuum). What is a
characteristic that we should look for? Tank volume?

Kohler Wellworth is a good choice. I've replaced 2 of our terrible early
90's era low flow toilets with these and am very pleased. I have also tried
the American Standard Champion, it's also very good, but does not wash down
the bowl as well as the Wellworth. The Champion also has a loud "clunk"
when the handle is pressed that takes some getting used to. I ended up
replacing it with a Wellworth because the Champion required constant bowl
cleaning.

-- Paul