I'd recommend taking your car seat. It's an additional cost if you end up checking it (or if you weren't planning on getting him his own seat but decide to do so after reading these responses you may have the additional cost of his seat!) BUT it's so worth it. It gives him something familiar and comfortable. Plus you have _no_idea_ what the car rental company's car seats have been through! They are unlikely to have instructions on how to install them, and the car rental company's employees will not help you. Stick with what you all know is comfy, clean, and safe to install.
I'd pay for him to have his own seat and take his car seat on the plane - once again, it gives him a familiar place where he's used to being strapped in. We took our daughter on her first flight at 18.5 months and were very glad we had her car seat for the flight and the rental car.
As far as housing - check out VRBO.com. It's a site where owners offer their vacation rentals directly to you. I am not sure how their prices compare, but you might be able to find a great deal on a house, so it's worth a look. It's secure, so you don't have the concerns of being scammed like you have on Craigslist.
Also, clarkhoward.com has a page on money saving tips for travelers. Here's a link: http://clarkhoward.com/liveweb/shownotes/category/10/104/ There is a lot of information there, some of it irrelevant to your travel plans, but hopefully you'll find something helpful!
Have a great time! I'm jealous! :)