Most baby sweaters are cardigans, it’s hard to get a pullover on a small wiggly baby. Lion’s website has lots of baby patterns, some in their cotton yarns. You want to try and match the yarn weight - worsted or sport or whatever - and find something that uses a similar size needle as your yarn. You can put ties on instead of buttons.
I’d also advise knitting at least a 6 month size, for most babies they’ll be able to wear that size at about 3-4 months. You’ll get tons of newborn sizes that the little will probably outgrow before he/she gets a chance to wear it more than once.