any of the Dr Seuss books

I was going to say Dr Seuss too. Early learner Dr Seuss are great 

Are you my Mother?

A fly went by

Diggiest Dog ever

A Bears Picnic

All of the above have good rhyming sequences so they can 'read along'.

Hairy Maclarey books.

Bamboozled, by David Legge.  Unlike many kids' books it can also be enjoyed by adults.  Awesome art work.  Out of print, at the moment, I think, you may be able to get it on eBay.  

I used to take my son into one of those bookshops you can sit down and drink coffee and READ the books and let him pick out his own.  That was so much fun ... an outing, and he got to choose ... 

And, at three, libraries are another good option.  

And (one more time) ... audio books are another thing to look at.  

And, (sorry), do they have eBooks for kids?  

Possum Magic

That book about the caterpiller (can't remember its name...)

The Very Hungry Caterpillar 🙂

Hairy Maclary from Donaldson's Dairy

Hairy Maclary and Zachary Quack

Hairy MacLary's Bone

Spot the Dog books.. not sure if they would still suit a 3yo.

I have a three year old grandson and he adores dinosaurs.........and the traditional nursery rhymes that you can sing and do the actions too.