DH and I are flying from LA to Boston next month, when DS will be 16 weeks. We are debating whether to buy him his own seat or let him go for free and hope for the best. I would prefer to get a seat and make our lives easier, but DH wants to save the money. Thoughts? If the flight isn't full, could we end up with a free seat anyway? We're flying on random weekdays, so we hope there are seats. We will need to bring his infant car seat on the trip with us no matter what...

Any additional travel advice is also welcome!