[Sprint Samsung Galaxy Note 3] topherk:
Well, I always recommend a full wipe (data, system, cache, dalvik) when flashing ROMs. I haven't wiped my internal storage or external storage since I got the phone, so that's not really necessary.

I don't think that unrooting your current ROM is necessary. Flashing the ODIN OTA update will automatically remove root access, so that's not an issue. Here's the steps I took when I updated to NH7 and installed my current ROM (see my sig):

Make a Nandroid backup.

I always do this just so I have a "record" of what I left behind. It also allows me to have all of my app data that I can restore via Titanium Backup (you have to buy the Pro version in order to restore specific apps from a Nandroid backup). I always store a copy on my ext. storage and on dropbox.

Do a full wipe

As I mentioned above, I always wipe data, system, and the caches when flashing ROMs. While I have to take some time to get the new ROM exactly as I like it, it minimizes any potential FCs and errors that some people get when dirty flashing.

Install NH7 all-in-one via ODIN

I installed the NH7 via ODIN. Please note that this is the fully stock, unrooted ROM and will also install the stock recovery.

Let the phone boot and connect to Sprint. Update Profile and PRL.

I do this periodically whenever I go back to stock (from AOSP). I rarely have connection issues, but updating the PRL an profile can help with those.

Install a custom recovery using ODIN.

My recovery of choice is TWRP, but others have found just as much success with CWM and Philz. Just make sure that you're installing the correct version of the recovery (4.4.X version, not the 4.2.X version). I always reboot to the main system after installing a recovery, but that's up to you. In the rest of this post, I'll say "TWRP," but I really mean "custom recovery."

[OPTIONAL] Make a Nandroid backup of the stock ROM

I always do this, but I recognize that it's not necessary, especially since we can just ODIN back to this image at any time. I just like having the option of having a stock backup on the device (in case catastrophe strikes while I'm away from a computer).

Use TWRP to flash your AOSP ROM of choice.

If you haven't installed any apps or messed around with the settings, you shouldn't have to wipe before flashing, but (in case you haven't noticed by now), I tend to err on the side of caution, specifically: wiping everything (data, system, and the caches) before I flash anything.

Set up the ROM how you like it and [OPTIONAL] make one last Nandroid Backup

Whenever I set up a new ROM to the exact way I like it (statusbar settings, accounts set up, apps installed and configured, etc), I make a nandroid backup of my device. This allows me to go back to that "fresh" image whenever something happens to the device and I don't have to muddle around fixing those minor tweaks. Again, I tend to err on the side of wiping the phone too often and taking too many backups, but I've rarely had issues with my phone and ROMs because of it (to the point where I can spend most of my XDA time helping others with their phones), so it might be prudent to follow the advice.

Anyways, that's how I upgraded to NH7 and installed a custom ROM. Others may take a less conservative approach and you're welcome to adjust any of the optional steps.

Hope this helps!

-Topher