If your Mom used it for years without problems, you have her magic touch and the 306 will work fine. It's your Mom's, it may be hard to part with.

I like Singer 306 machines. If you can find a good variety of disks you can do a lot with one.

I agree with JMiller, clean it up and bring it back to life and think that you are doing the same with your mother's behavior.

Take SteveH's advice. froggyintexas

Oh me, I am like you here; pulled six ways to Sunday. What do I do? What do I do? You ponder on it, and whatever hits you just right at just the right moment, go with it, and don't look back. Much good advice has been given here; but you are the one who will benefit in the long run. Let us know how you work it out. I'll be watching.

I like them too. I do prefer the 319/320 (which use the same needles) but only because they have some patterns built in. They're a very good machine, and extremely strong.
The 3-in-1 oil is bad for sewing machines (leaves deposits that gum up the works), so you might want to clean it off using kerosene (the 1950s and best way) or diluting it by changing to regular sewing machine oil or tri-flow: With regular maintenance the deposits shouldn't turn to gum.

If you were in Australia I'd have a full set of pattern discs for you :)

Take it, clean it, and if it just doesn't feel right sell it or trade it for what you want