I have an Agri-Fab 18" Silent Reel Mower and it is excellent. Like most hand tools from a previous era, cheap mowers do not function well.
A key feature of the Agri-Fab mower is that the two blades (stationary and fixed) do not touch. They are separated by a few thousands of an inch. Without the blades rubbing together, the mower is easier to push and the blades stay sharp longer. The adjustment mechanism on the Agri-Fab mower is very good, which makes adjusting that gap between the blades easy and precise.
I would not buy any of the mowers offered at the big box retail stores made by American Lawn Mower Company, Great States, or Scotts. They are all made by the same company and they all use blades that contact each other. Everyone I know who has tried one of those mowers gave up after one season or even one mowing. If you really want to use one, then buy one for cheap off of craigslist.
When mowing St. Augustine, the blade height is very important. St. Augustine likes to be very long. The maximum height on my mower is 2.25". I wish it were a little higher. If you have St. Augustine, then blade height rules out Brill mowers, even though they seem to be very well made.
I have never seen one in person, but if I were buying a new mower today to, I would also consider a NaturCut or a Fiskars. The website peoplepoweredmachines.com has some nice comparison charts.