singing in private is not the same as singing out.

Use basic keys of D C G and learn the chord families

a capo will prove useful as migyt a tuner ,to save time as well as to tune the guitar.

familiarise yourself with at least a thump pick if you intend to use the fingers, finger picks depend on if you play a steel strung job or if you have good nails.

Concentrate on the singimg and play quietly

The secret is to play everyday.

Good luck