What to look for in a new/replacement toilet?
There are some articles that speak to the minor differences between a class 5 and 6 toilet. The most important thing to know is that a class 5 toilet has a larger diameter trapway and the interior of the trapway is polished like the inside of the bowl is.  They also use a faster low water volume flush system.  The common complaint is that solids can leave 'skid marks" on the bowl as there is not a large volume of water in the bowl after flushing. the class 6 uses the same flush technology, but has more rim water action to wash the sides of the bowl better. Most reviews I've read say there really isn't much difference at all. 

The better units are the Toto Drake series, the Kohler Cimmeron and American Standard Cadet series. They all can be purchased for between 200 to 300 dollars. Round bowl standard height is cheapest, elongated bowl comfort height being about 30 to 40 dollars more. 

Even though we aren't suppose to endorse brand names, I will say, I have installed a couple dozen Kohler Cimmerons in private homes and in my apartment buildings. I have had a few complaints about the "skid marks", lol, but have never had a call about a clogged toilet. These things flush like a tidal wave.  

The other feature I really like is that the tank always is at least half full.  With average use, the water comes up to room temp and a flush only introduces 1.3 gals of new colder water.  The result is no condensation on the tank during the hot humid months of summer or when the bathroom becomes a sauna after a long hot shower.  

I have also installed the more expensive (under $400) Kohler Cimmeron one piece, elongated, comfort height in my own home. Looks good and works great if your looking for that low tank modern style.