A lot of this is personal preference, where you live, how much money you have and what makes you feel appreciated though?
DH doesn't like buying online, preferring to choose and buy in person (I'm similar). He doesn't drive and the small town we lived in didn't have lots of shops. We were struggling - I was in hospital for 10 days for the birth and aftermath, then developed severe PND. Him going off on a jaunt to a different town and shops wasn't an option. I wouldn't have been capable of getting the pram out, boarding a train and joining him. I do drive but driving to a different town, with a newborn just to choose a present, would have been insane?!
There is no way we'd have bought a present like this in advance - high risk pregnancy, friends have had stillbirths. We didn't even unbox the pram just in case it ended up being returned.
He bought me jewellery previously (when I completed a professional qualification) and spent ages choosing it. It's something I wear everyday. I don't wear jewellery other than that, wedding/engagement rings and watch so no point getting me more.
His work only paid statutory paternity and we were on a very tight budget for maternity leave. Buying jewellery in the run up to this or during maternity then childcare costs would have been irresponsible.
There are so many threads on here with deadbeat partners who don't pull their weight. If you want a push present then I hope you do get both that and a useful partner but I know I couldn't have cared less about a push present.