It's not uncommon for thicker glass be annealed, not tempered, for a table top. This is due to the amount of force required to break it.
From what I've been told growing up around a glass shop and working in the industry for a number of years, the reason glass cutters work is that glass, stone, etc will always break at the greatest point of stress.
When you apply pressure to the surface of the glass with a glass cutter you are crushing the surface under the wheel which causes heat. Oiling the wheel on your glass cutter will help maintain this heat evenly for a longer period of time. You need to break the glass along your score before it cools in order to get the most reliable break.
Thick glass, 1/2" and greater is very difficult to cut even for the very experienced. It also takes a much greater force to break after scored. If this is your first attempt at cutting glass I would recommend getting a few scrap pieces of thinner material and practicing on those to get the feel for scoring and breaking the glass. The thicker the glass the harder it becomes to cut off a small amount. Even 3/8" can commonly break roughly and required a belt sander to polish the edge smooth. Breaking 3" from a 1/2" thick piece of glass will be difficult and I would personally opt for a wet saw.
Also, any time you cut glass the edges will become sharp. Be sure to use sandpaper to smooth the edges, called a seam, in order to help prevent cuts.
As far as cutter brands, I prefer Silberschnitt because the brass has a nice weight to it and I've grown accustomed to it. Fletcher is probably the most common brand I've seen from shop to shop. Someone that cuts glass daily is more likely to go with a cutter that is self oiling and is filled in the end.
The cheaper "hobby" cutters do the job just as well. The most important thing is the wheel. A carbide wheel will last you longer, but for limited usage a steel wheel will suffice. If you opt for one of these types of cutters be sure to rub 3-in-1 oil on the wheel prior to scoring the glass.
A hone angle of 140° is the most common. After enough experience 140° is easy enough to turn when needed, but broad enough to be effective for 1/4" or 3/8". I've used it for glass with a thickness up to 3/8". A hone angle of 154° is what is used more commonly for greater thicknesses. This angle will give a broader score allowing for more surface stress distributed along the same line allowing for a more reliable break. A 120° angle is more often used in artwork and difficult pattern cuts. A more acute angle is easier to work with and what you want majority of the time. The greater angle is more difficult to work with but necessary to control a break on thicker glass.