Second the idea of a toy to push around. My one year old loves to push his lawnmower and his shopping cart. He throws small toys in the cart, pushes it around the house and takes the stuff out. He could do this all day. Toys that help with fine motor skills would be good too...stackables, blocks, push button toys, pop up toys, etc.
Re: 1st Birthday Gift
Around $50? Don't mind spending a little extra.
Cozy coupe is around 50 on Amazon. There is even a pink one.
Tunnel. Around 25. https://www.amazon.com/gp/aw/d/B0032MYYBE/ref=mp_s_a_1_1?qid=1374158081sr=81pi=SL75
Any little people sets. My son especially loves the bus.
Mega block sets.
Water table. My son has the Little Tikes pirate one. It's a hit.
Something to push around. Shopping cart, lawn mower or vacuum cleaner.
Good luck! If you go to any toy store I'm sure they could give you ideas as well.
Thanks!