Library Time

I usually pick a few books off of the list and try to get at least one per child and then I let each child pick out one book of their choice. You can find lists of age appropriate books at the library website, or just google age appropriate books. For me, I just pick a Genre and grab a few books...if I like them, great and if not, I wish myself better luck next time :)
I have four kids ages 10, 6, 4 and 1 1/2, so I do know the trials and tribulations of taking kids to the library, but it is something I would NEVER give up.

I agree that library time can be stressful. My two kids (4 and almost 2) love the library, almost to a fault. They run and grab and just are overwhelmed with happiness. We do just grab the random books and I try to take a glance to see if it is appropriate or not (meaning reading level, really). I think having a system helps us. How we return our books, how we carry the books while we are looking, how we take turns giving mom a book, and then how we take turns helping to check out. It took time for us but now that we have a routine that chaos is better.

Good luck!!

If you want help in choosing great books for kids, do an internet search using "reading list children". This will give you loads of ideas. You can reserve books to save time, and just run in and pick them up. Caldecott and Newberry Award winners lists are great too. The children's librarian can be a big help too.

Speaking as a former librarian, letting your kids choose is a great way to know what might be interesting to them at the time--usually with an 18 month old, it's baby and adult faces, and more pictures, fewer words; for a 2 1/2 yo, it's probably a certain subject like animals or trucks. Caldecott award winners are good but not usually for that young of kids, and Newbery winners are for literature (no pictures!). I would really encourage you to talk to the children's librarian at your local library to see what she or he thinks. My 2 year old loves Maisy books by Lucy Cousins, Richard Scarry books with all the cars and trucks, Byron Barton books, and Rosemary Wells books. Really almost any board book will work for them--I'd steer away from the hardcover books with pages that rip easily.
Good luck!