Thanks guys! Your responses are helping me sort this out.
From what I gather, the Note 4 is a powerful device that is still relevant in 2016, but it will only be losing official and community support from here. Jumping from the Note 3 to the Note 4 will not be a big upgrade by today's standards. In the long-term, it would make more sense to buy a newer device that will outlive the Note 4's firmware support.
However... I love the s-pen, micro SD card, removable battery, and size of the Note 3, which is my first smartphone. I won't get all of these features in another phone again except for the Note 4. With an attractive, smooth, and stable custom ROM installed on the Note 4, it could probably satisfy me for a long while. I wouldn't have to worry about a deteriorating battery. The hardware is aging, but the specs are more than powerful enough for what I'd ever use a phone for.
I've been jumping back and forth between these thoughts. Your responses make me lean towards waiting to buy a newer device. The phone must support at least up to 64gb of storage (internal or expandable), have good developer support, and cost no more than $400. Aside from the Note 4, the OnePlus 3 fits my requirements. The only drawback is that it doesn't support my carrier (Verizon), so I'd have to look into switching. I may wait and see what the Nexus Marlin is all about. It probably wont fit within my current budget, but I may be able to work something out if it really appeals to me.
Thanks again, and I'm always open to more suggestions.