body fat measurements

The Body Composition Monitor is rather accurate, although you must be empty of all things in order for it to work correctly. Any water or food inside you will be counted as fat. When I was in hospital, they'd measure me with it both in the morning and straight after lunch - the difference was tremendous.

It really depends on what your looking to get from the measurement. If this will be a regular measurement, like every week or so, then you can go with any of the ones you listed. The accuracy becomes a little bit less of an issue if you look at the overall picture the data is giving you.

Calipers are less affected by hydration/food/waste in the body, but will require you to have some help from someone who can remember the exact spots from time to time.

The body fat scales/hand held devices are easy to use and don't require a second person, but have more fluctuation due to the amount of fluids in your body at the time.

Measurements can mostly be done by yourself, but are prone to bigger errors from time to time. They are the most inexpensive and you can plug the numbers into multiple calculators and average the results if you want.

Bodpod, water displacement, or dex scans are a bit more accurate, but can be difficult to find/schedule and cost a bit more. They would not be a frequent measure of progress, but you are more likely to find the actual BF%

I have a body fat scale that does bioimpendence and I find it to be enough for my needs. I step on it around the same time each week after waking up just before my morning shower. Each week I take the numbers and plug them into a spreadsheet to track them. I also do a little breakdown where I take my weight for the week and multiply it by the BF% to see the body fat in lbs and the lean mass in lbs. Breaking it down like that lets me track the composition better and get a good sense if I am on track by losing body fat and keeping lean mass weight mostly stable.