Which is correct or preferred English?

[Beswad]

For beauty business.

'No appointment needed'

'No appointment require'

'No appointment necessary'

[mike11111]

If you mean "required" in no. 2, then all are equally acceptable as they all say the same thing. However, if your business takes off, then you may have to reconsider.

[Beswad]

@mike Thanks I did ment to type 'required'.

[mike11111]

Actually, thinking about it, if I were a business person, which I'm not, I would specify appointments necessary, as it gives the impression that your services are in demand. You could always add at the end of your advertising something on the lines of, "Valued clients may be seen without appointment, depending on the exigencies of our operations". Bullsh!t I know, but what the hell if it brings in extra custom.