Yes, the 105032 is supposed to be the bobbin case for the 306. It also takes "L" bobbins, which can be found prewound many places online. They also can be found at
https://shop.sew-classic.com/Bobbins...ack-55623S.htm and https://www.sewingpartsonline.com/bobbins-universal-deep-groove-10pk-55623s.aspx?
Sometimes this machines have been altered to accept 15x1 needles, but my guess is that probably your machine hasn't been. The needles can be found at
https://shop.sew-classic.com/206x13-...eedles_c46.htm and https://www.sewingpartsonline.com/10...-s206x13.aspx?
A manual can be found at
https://www.singer.com/sites/default/files/outdated_product/SINGER%20306_306K%20and%20306W%20Sewing%20Machine. pdf
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