With my 2.5 year old I started Sonlight P3/4 books - see
www.sonlight.com - they are all good stories but start out very short and gradually increase in length. By the time she had finished these stories she was ready for longer picture books and also early chapter books. Her attention and concentration grew greatly over this period of time but I did need to read the books in the order given by the instructor's guide because she was younger than their recommended age for the curriculum.
From 18 months to 2 years we used a lot of board books, lift the flap books and touchy-feely books as my DD was still so tactile. Bath books and cloth books also worked well even though we had been reading these since she was less than a year old.
My 13 month old is enjoying touchy feely books now too, but she needs very very short books to hold her attention - often we just hear the first few pages and then she is off!
Book names we liked:
Any of the Hairy MacClary books
Julia Donaldson
Mess Monsters and Mess Monsters in the garden
Harold and the Purple Crayon (and other versions of this)
If you give a mouse a cookie
Children's Non-fiction books about animals and their babies (she wanted a lot of information on this - more than an average 2 year old)
Shortened versions of fairy stories (We read the Ladybird Read-it-yourself to her at this age)
Each Peach pear plum (?)