Welcome VARam1500.
I have both machines, but haven't really done much with either one. I do know that on most vintage machines the advice has always been to hold on to both threads when beginning to sew. One can sometimes get away with not doing that if you sew on a scrap of fabric after finishing a seam and leave the scrap attached. That leaves an anchor of sorts. Do you have manuals for either or both machines?
One of the manuals I have for the 306 says to "Lay both threads back under presser foot diagonally across feed ... so that when the presser foot is lowered the threads will be firmly held between the feed and the presser foot." I just hold the threads behind.
I know there are some differences in bobbin cases and much discussion about on some forums. I also know that there are some discussions about different bobbin cases and altering to be able to take a 15x1 versus the 206x13 needles that were the type of needles are the original needles used on these machines.
I don't know if it will answer your questions, but you might want to look at
https://shop.sew-classic.com/Bobbin-...ils-173058.htm and
https://shop.sew-classic.com/Singer-...ils-105032.htm that I found via
https://shop.sew-classic.com/Bobbin-Cases-Parts_c23.htm
Good luck.
Janey - Neat people never make the exciting discoveries I do.