I have made some knitted stuffed animals for babies. Teddy bears and even dinosaurs. You might want to try something like that. Family Circle Easy Knits for Babies has some great patterns. Maria
One of the gifts I loved most when our son was born was a soft white baby blanket that one of my MIL's friends knit for us. I was in my extended "away from knitting for two decades" phase, so it wasn't even that I was a knitter and was loving a knitted gift! It was just that it was the perfect small size and beautiful. We used it all the time and I tucked it away for grandchildren some day. So don't give up on a blanket too quickly. I also think a knitted toy would be wonderful. And the washcloths. And the mitts. And ... well, you certainly have a lot of knitting ahead of you, don't you?
One of the most popular ideas I ever had and passed around was to knit a toy and to use a terry type cotton yarn. Really simply flat shapes and then stuff the toy with sut up and crumpled plastic bags. Fun fur would work equally well or maybe a nice chenille. This gives interesting textures for the baby's hands to explore and the crumpled up plastic bags (especially the strange papery kind) makes interesting crackling noises when squeezed. I don't remember who I did it for, but I knit someone a set of blocks in different yarns, a different texture for each side and a little bag to carry them in. That was really successful.