I would get a bag of Mega Bloks. That's what I got my oldest for his 1st birthday. They are useful up until about age 5. Toys like this encourage creativity and spatial skills. There are "girl" colored pastel sets if you want those colors.
https://www.target.com/p/mega-bloks-first-builders-big-bag-of-blocks-toy-blocks-with-storage-bag-130pc/-/A-91960695#lnk=sametab
More than just board books, I like books that have little activity tabs, mirrors, textures. Those are interesting to that particular age.
Buying for a one year old is tough because they change completely from age 1-2. Most objects greatly suitable for them right now will be irrelevant in 6-9 months. I would look at toys for 2-3 year olds and be sure they cannot be choking hazards (e.g., my son who never mouthed anything else once bit a chunk out of a Nerf football right in front of me - the football is not a chokable size but the material made it a possibility).
Give gift receipts. Parents get duplicates and things they don't have room for. This is the most efficient way of balancing the desire to give a real gift with not being wasteful. Target is a great choice because it sells bany consumables.