1. Having a J-1 waiver approved definitely will prevent you from extending your current status. The same very probably goes for when it gets rejected, since the mere act of applying for it shows that you do not intend to abide by the purpose of your J-1 program (i.e. return home).
2.The best time is either 1- after you have obtained your last possible extension on your J-1 or 2- you have an H-1B offer waiting at least 6 months down the road. If you don't have a H-1B / green card job waiting, then its safest to max out your J-1 renewals before applying for a waiver. If you look for a job, make sure that your position is secure with enough time (6 months to be safe) to get a waiver completed. It is also important that you secure a job at least 6 months before your J-1 status expires; otherwise your status may expire before your new paperwork is complete.
Finally, if the DOS needs your sponsor views in order to process your J-1, keep in mind that your own institution may require its own policy. For example, my US sponsor will not respond favorably to a DOS request for sponsor views unless I have an actual job waiting for me elsewhere inside the US. Keep that in mind as well, although this may be different / irrelevant to your situation.
