I have so many different carry solutions/options, it's insane. But that's mostly because I learned long ago that there is no right answer for every situation. Here are the various options I'll use, depending on the park, the day, and what I intend to shoot:
1. Simplest method - camera with one mounted lens on the strap around my neck, shoulder, or wrist...no bag or extra bits. If I'm confronted with potential for rain, I might stick a large freezer Ziploc bag in a back pocket so I can throw the camera in there in a pinch.
2. Next lightest method - Spider Black Widow belt holster. A small piece screws into the tripod mount on the camera, and slots into a small belt plate that sits on my belt, so I can grab the camera on the go but leave my hands free. Very useful for when I want to shoot with two cameras but travel light - one stays in my hands while one is on the holster, and I can swap them as needed.
3. Next - small Tamrac video camcorder bag. This is designed originally for the old mini-DV camcorders, but happens to perfectly fit my DSLR with 18-250mm lens, plus one more small lens like my 30mm F1.4. I can generally bring one camera & lens with one extra lens and room to fit the camera in a rainshower, or one camera & lens with two extra lenses but the camera has to stay outside the bag with one lens mounted.
4. Next: Tenba shoulder bag - this one is larger, and can fit up to one DSLR with mounted lens and 4 additional lenses, 2 camera bodies each with a lens, and 2 additional lenses, or any similar combination. I use this often when I want to bring both my cameras with me plus an extra few lenses, and still have room to stuff it all away for transport or rain protection. It's still not a huge bag - about the size of a toaster oven.
5. Next - Think Tank holster bag. This is a specialty holster that can handle two very long lenses side-by-side - I use this mostly when I want to shoot with longer lenses - I'll occasionally use it at Animal Kingdom where I can bring my 300mm F4 and TC combo, and maybe my 18-250mm and 10-24mm or 30mm stacked in the other holster. When I'm out birding, I'll bring my 300mm F4 and 200-500mm lenses together, with one mounted on camera and the other in the holster - I can easily slot the mounted lens in the empty chamber, release the camera body, and mount the other lens to switch between them without having to put anything on the ground.
6. Finally - the big solution, when I need to bring almost everything - Kata R102 backpack. This can handle various combinations of up to 2 camera bodies and 7-8 large lenses, or up to 12 smaller lenses. It's my main travel bag that I carry most of my gear in on planes and such, and will bring most of my gear to Disney in this bag, but it rarely goes out into the parks as most of the time I only need at most 3 lenses at my disposal for each camera body, and bringing the large bag would just be overkill.