Traveling With Infant

I've been soliciting advice on traveling with a newborn since before my daughter was born 😂🤦🏻‍♀️We are going on vacation at the end of May and I'm trying to gather as much information as I can to try and make things as smooth as possible.
My question {this time} is this: Once we arrive there is a 3 hour drive from the airport to our vacation home. Meaning we will have to rent a car. Is it easier to rent a car with a car seat or to check your base and car seat with the airline? Both seem like a hassle lol. I'm worried that in addition to being expensive and inconvenient, our base and/or car seat will get damaged by the airline. However, if we rent a car with a car seat, I'm not sure what brand/ how safe it will be. Also, I have the Keyfit stroller caddy that our carrier pops right in to (LOVE it) so if we end up renting I will not be able to use our stroller for the whole vacation.
For mamas who have traveled-Please leave your advice on this as well as any other helpful nuggets of wisdom for airport travel! Thanks for your help!