Our first bday gift to each girl was a photo book of their first year. DD1 loves hers now that she's old enough to understand it. Typically it's something small, but it's something they like/want. This year dd1 got a new book and a bag of legos from a garage sale. She loves them and we enjoyed watching her open them. Last year it was books and puzzles. As the years go on, I'm sure it will change I don't have hard and fast rules, but there will be gifts.
Yep birthdays mean gifts. No matter the age. For their first they get an anywhere chair.
This is what I'm planning to get DD for her first birthday. We only got her a couple little things for Christmas because she already had pretty much every toy appropriate for her age. We do plan to have a big birthday party, but I think that's more for us than her.