The Avent cups are fine without the valve. DS got to the point where he refused to drink out of a non-spill cup because he couldn't be bothered. But after he chewed up most of the Avent green and white spouts (plus the ones I had replaced) I gave him ordinary sippy cups. He's been on proper cups/straws/juice cartons since about 21-24 months.
DS stopped his bottle at 12 months but has never taken as much milk out of a cup and now never really has any. So this could be a down side of stopping it early especially since we always cleaned his teeth afterwards. It was bath, bottle, teeth, story, bed from 6 months when I stopped breast feeding.