Well, you never have to worry about the apps themselves when it comes to new hardware - iTunes knows which apps you purchased, and they're generally backed up to your computer via iTunes. Whatever you do with the new iPad it will be possible to get the apps you paid for onto it without having to repurchase them.
The data of the apps, on the other hand, does not transfer over automatically if you do a clean install. The data of the apps would be things like your place in a game level, or the files you've created in a music notation app, etc. You have a couple of options: you can do backup of the iPad 2, and then restore to the new iPad, and that will bring the app data across to the new hardware. Alternatively, you could purchase a Mac application like iMazing, which is purpose built to allow you to save/manipulate/restore app / music / photo data stored in iOS devices.
Photos are essentially app data for the Photos app, so what I wrote above applies to photos as well. You do have some other options for photos as well: you can use Image Capture to grab photos off your old iPad, stuff them into a folder, and then tell iTunes that you want that folder stored on the new iPad as album you can view (it won't come in as part of the camera roll, however). Or, you can put photos in the (Mac) Photos app, turn on iCloud photo storage, and have it shared to all your iOS devices.
Personally, I've never had a problem doing a backup and restore to new hardware. I generally do a backup and full restore every time I do a major iOS firmware update, which is pretty frequently. I wouldn't think that you're going to get a lot of benefit to starting over completely on app data, which is what you're doing when you choose to setup as new iPad.