opinions (but no nastiness please)

i'm not going to tell the whole story because i want everyone to actually read and answer, but i need your own personal opinion. my daughter is 3 1/2 months old and her father is filing for standard visitation (after questioning paternity for around 5-6 months). he saw her sunday for the first time in 6 weeks so i'm asking that he has supervised visits first, then day visits, then an overnight occasionally, THEN standard visitation. he's fighting back because he wants standard immediately.. he claims i never let him see her and that i questioned paternity. i never ONCE questioned paternity, or i wouldn't have taken the freaking pregnancy test in front of him. i never ONCE denied him the opportunity of seeing her. even when i was in the hospital he turned down the chance! i've always said "give me 24 hours notice and you can see her when you want." i even have text proof! am i asking too much from him? i'm trying to make this as easy as possible on her, he's a stranger to her. when he saw her earlier this week he kept kissing her face and she wouldn't stop crying, he had no idea what to do with her and she had no clue why this stranger wouldn't get out of her face.. i want to make sure they know each other and he knows what he's doing. am i asking too much? am i right for trying to ease into this? this whole time it's been about what he wants, not what our daughter needs. i'm so worried and stressed about this. send some prayers/positive vibes my way for peace and comfort please! as well as opinions. and if anyone's been through this share your story please! 
i want to add that in no way am i keeping her from him. i want him to be part of her life, i just want to make it as easy as possible on everyone