Disc transfer help needed

I recently found some 78s of my parents' singing that were made in the early
1940's.
They were apparently recorded at home on a portable machine. Record labels are
Audiodisc, Wilcox-Gay and Howard Home Recording Disc.
I'd like to transfer these to a CD and clean up the sound.
My record player is classroom-style portable from the 50's or 60's (Rheem).
What's the best way to do this?
Is there a specific type of needle that works best?
Turntable adjustments or considerations?
Any treatment or cleaning of records? The edge of one had been bent.
How about skips?
Should I use phono-plug line-out straight to a mini-disc recorder, or is it
better to record the sound of the record player's speaker?
Are there any programs that work best to clean up the sound in these
situations?
Your ideas would be most appreciated.
Thanks,
Joe Nelson