I am by no means an expert and I am just starting out but I can tell you why and how I created my anti-backlash nut.
I chose the compression spring method because it seemed fairly easy and cheap to setup. And it is cheap too. The parts are readily available. The only drawback to using the compression method is that the nuts and lead screw need to be replaced on a regular basis because the compression causes the nuts and lead screw to wear faster. No problem because the system is cheap and easy to replace.
I use 1/4-20 threaded rods for my lead screw. Lowes has inch long 1/4-20 nuts that are 3/8". A 3/8" socket fits them perfectly. I attach two wooden blocks about 2" a part on the bottom of the table. Mounted into each wooden block are the two 3/8" sockets. Both of the sockets are glued into the wooden blocks. One one of the nuts I place tape around it and press it into the socket to eliminate play, the other nut is left to free in the socket. I then thread the lead screw on with a spring between the two nuts.
As for how much compression I use? I figured that there is a relationship between nut/lead screw wear and spring compression: the higher the compression the greater the wear. I use justed enough compression to eliminate backlash.
Hope this helps but like I said, I'm not an expert and a nube.