Note that with the most recent versions of iOS (I think since iOS 5), you can do over-the-air syncing on your wifi network. You do have to do the first sync with the local iTunes library through the USB port. There is a setting on the iPad and on iTunes (on the general settings tab of the device settings in iTunes) to enable wifi syncing. Once you do that, every time you plug the iPad into the wall to recharge, if the computer and iPad are on the same network, and iTunes is running on the computer, the sync will happen automatically. The most important part of that is backup, since it sounds like you don’t keep much in iTunes. The backup is mostly of application data, by the way, since the apps themselves can be restored directly from the cloud–Apple knows what apps, songs, books, and videos you have purchased from them, so they can be restored automagically if you buy a new device or need to reset or replace the old one due to problems.
We have multiple Macs, an iPad, and everyone in my family has iPhones. Pretty much none of us ever use iTunes on the Macs except for occasional backup. There is no real need to transfer documents most of the time. I vote for the Dropbox solution for sharing docs (including mp3s). You can use the Dropbox app (free), or just share a link which you can open in Mobile Safari and view or play in the built-in viewers (which handle every common document type I’ve ever dealt with, including MS Office documents).
There are also tons of free and low-cost apps that integrate with Dropbox (and other cloud services) and provide nicer interfaces for doing the things you want to do, including document editing.
As far as post-processed photos, I don’t do much of that, but I do know that if you plug an SD card directly from a camera into the SD card reader dongle, it will automatically download everything to the Photos App photo library (not iPhoto–that’s a separate, paid app that supports a lot of simple post-processing tasks). There are lots and lots of apps that can access the built-in photo library to mess around with the pictures.
The idea of every app having its own document silo is only partially true. You need not use the Music, Video, or Photo apps that are built-in. Their data is accessible through public APIs, and there are many third-party apps that are superior to the built-in ones. Also, the Apple Podcasts app is an optional, free app, and is currently not that great. Use Podcaster, Stitcher, or any of a number of other apps instead.
Hope that helps.