There are ratings and reviews of toilets available on the internet.
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I went with a Toto Drake back in 2007 or 2008 (before the Drake II was listed). The previous toilet was constantly being clogged and having to be plunged. The Toto flushes very well. It has a dual flush thing where the shorter duration does a quick flush using less water (ideal for no toilet paper in the bowl) and holding the lever down for a bit longer does a full flush. The only clogging issues I had were related to plumbing beyond the toilet.
The only cheaply made part was the toilet lever. The lever itself was ok, but there was a plastic piece inside that breaks somewhat easily. After being the sole toilet in use for a few years, the thing finally broke. Fortunately I have another Drake sitting in a box waiting for the completion of a bathroom remodel so I took the lever off of it. That boxed one got a Gatco adjustable lever that I got at a clearance sale.
The Drake I does not have a bowl wash though. I've heard the Drake II is better. It comes with Sanagloss coating and a type of bowl washing action so it is supposedly easier to clean. My Drake had Sanagloss, but unfortunately I have very hard water that comes out reddish brown tinted and it stained the inside of the tank and the bowl.
According to Terry, the best bang for your buck is the Toto Drake II. It comes in elongated ADA height with Sanagloss. ADA height is so much nicer than regular height.
The original Drake is still nice as well. According to MaP testing, it can flush 900 grams.
The Drake II flushes 800 grams if it is a two piece. The one-piece flushes 500 grams.
(Anything 500grams and up is good).
The Kohler Cimarron mentioned above flushes 800grams but does not have a bowl wash. It only had a three star rating (or in this case, hearts).
The only Briggs toilet listed was the Vacuity and it was not recommended. It had all sorts of problems. Clogging, constant running, and other issues. Many people were saying the Briggs toilets in general were just lousy.
The Drake II is more expensive, but from all accounts its a good investment.
Of course, finding a place that sells Toto is not always easy. They generally don't sell them at HomeDepot or Lowes, but Coburns usually carries them.
Terry's site had a printable guide that explains exactly how to install the Toto Drake. I imagine the Drake II is installed the same way. We were able to put the Drake in ourselves with the guide.
Oops, not trying to advertise that site, I just like it and this one.