I gather this is your Mother's machine? That is nice that you have it. Does it have the smooth finish or the rough finish? My 306W has the rough finish. I don't think mine actually had a top. Mine is in a wood base, with no hardware on the ends. As a matter of fact, the hand wheel extends past the base, so that a top would not fit on it.
If it is a rough finish, it is sometimes called wrinkle, crinkle, or godzilla finish. As far as cleaning that type of finish, there are a variety of answers. With any product, be sure to test an inconspicuous place. I washed my hand pinker (a black crinkle finish) with a janitorial neutral cleaner and a toothbrush then wiped with damp rag, dried it and then used a Turtle Wax product that I don't think is available any more. John cleaned a White machine with crinkle finish with Windex, unbeknownst to me until after the fact.
There are at least two threads about cleaning this type of finish on QB.
How do you clean a Crinkle finish?
Cleaninf Gorilla finish
If you should search on QB, you will not be able to view the thread, until you refresh the page.
I'm not good at wood work, but I think the base should be able to be repaired and cleaned to at least be functional.
I believe there is a 306 manual at
https://www.singer.com/support (Not affiliated with link) It might show as a 306K, but should work for the 306W as the manual (not original) that came with my machine has both 306k and 306W on it.
Janey - Neat people never make the exciting discoveries I do.