I want to closely monitor my body fat % but I'm not sure which scale/device is best for doing so. Are the scales with built in boy fat % calculators or the handle measuring devices accurate and to what percentage?
Accurate? Against an objective measure like the water test? No?
Against itself? If you do it the same way every time then probably.
I use the same protocol each time. For me, it's early morning just after my shower. That way I'm getting consistent results and can then see the trend over time.
For most purposes that's just fine.
A DEXA scan is going to be the most accurate method of bodyfat analysis, but it's expensive and limited in availability. A properly done underwater weighing would be your next best alternative, but it is also limited availability and can be expensive.
The two most commonly available methods are skin caliper testing, where folds of skin are measured, and the thickness of the fold/pinch is recorded. The most accurate method uses 9 different sites, although there are 3 and 6 site measurement protocols available. This requires training and familiarity, and is easily done wrong. Done properly by an experienced tester it is a very good method, however.
The next commonly available are the bodyfat or Tanita scales. These use bioelectric impedence, or basically passing a very low level current through the body from one foot to the other. This can be thrown off some by body hydration, wet skin, other factors. They have an error rate of +/- 5% usually, which means it could be anywhere from 5% low to 5% high.
However, if you take some care to do the Tanita weighing under the same circumstances, then you can use the scale consistency to measure progress, since it will nearly always measure the same. By that I mean that if your scale measures you at 5% more than your actual, it will always do so. Couple that with the mirror test (Look at yourself in the mirror) and it's the most affordable and available, as well as being consistent.
If you really do need to closely monitor body fat, then I would recommend getting an underwater weighing or DEXA scan, then immediately afterwards get on whatever scale you want to use (Bring it from home), and compare the values. That way you know specifically how far "off" your scale is from a true measurement.