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.