Hi, Danielle! We almost always drive our car down from New Jersey to Walt Disney World, so in most cases, I have my car with me. There would be no charge to park your car - or a rental car - at your Walt Disney World resort, and you would be given a parking pass that allows you to park for free at any of the Walt Disney World theme parks.
I have always enjoyed the convenience of having my car with me. When the girls were little, it seemed easier to me to head right back to our car, fold up the stroller, pack in the bags, and head back to the resort. It also always allowed the freedom to grab a quick bite at a local restaurant or to pick up a few groceries.
Having said that, I've recently started using Walt Disney World transportation, and you really can't beat it for getting you where you need to go! As often as we have been to Walt Disney World, I am directionally challenged, and still get confused driving around. It's nice to just hop on a bus and let someone else worry about the drive. The wait can be long if you are trying to get a bus when the parks are closing, but I don't think we've ever had to wait longer than 20 minutes. They try to make sure there are buses added where they are needed.
I think the choice is a personal one, and it is doable at Port Orleans Riverside without a car. If, however, you anticipate needing to head outside of Walt Disney World property, or if you just want the convenience of going when you're ready to go as opposed to when transportation is available, then a rental car is a better option.