1) DO NOT register at Target. They have a VERY limited selection and they have a horrible return policy. They will only let you do a VERY limited number of returns without a gift receipt, but people never give gift receipts when they're buying off a registry because they know you want the item or assume you don't need one. Seriously, don't do it.
2) I would register in the store. I understand the appeal of doing it online... I did our entire wedding registry all online! However, with the baby stuff, especially big stuff lke strollers and carseats, I think it's important to see it in person and even test some things out. Also, you want to make sure that the items you are registering for are actually carried in the store and not just sold online. The whole point of including an actual store is that people can swing by the store last minute to pick up gifts, and they won't be able to do that if 80% of your registry is stocked with online-only items. Those stores have a much bigger selection online than what they actually have in the store.