I happen to be the proud new owner of a TI-84+SE. It's in excellent condition, came with all of the original packaging, cables, manuals, and CD, and does this when you press [Mode] [Alpha] S:

Yeah I'm pretty happy about that :)

Anyways before I go blundering off trying out games and programs, I thought I'd ask a few questions. There's usually a body of common knowledge surrounding these things, what to do, what's what, what definitely NOT to do, etc. I know basically nothing, so please do enlighten me.

What I want to know is stuff like the following:
What are the must-have games, apps, and utilities?
What OS should I be running?
Can you downgrade the OS, and if so how?
What shells/OSes are there, and which ones do what?
How do I not accidentally brick my calculator?

If there's any other tidbits of useful (read: will save you hours of suffering and frustration) knowledge, please do tell.

To get a basic scheme of what this calculator can do, reading of TI's official calculator guide(availavle on education.ti.com) would be the quickest way to achieve that.
About the questions you've mentioned, here're some of my ideas:

• Must-have programs: It really depends on your interests and use cases. As a 83+SE owner who is interested in on-calc developments, I have CalcSys, Mimas and DoorsCS installed; For calculator games, I find ZTris and BeNumbered pretty fun to play.
  
• About OSes: If you are using it for academic purposes, just go and install 2.55MP, which enables you with more(but not much more) math functionalities; If you want to have highest possible compatibility with all the community programs, you can install 2.43(it's the latest non-MathPrint version and MathPrint breaks a lot of stuffs).
  
• About downgrading: TI didn't bother to implement anti-downgrading mechanism for monochrome 83+/84+, until Boot 1.03, but that protection could be bypassed with a community-made program named "Unsigned", which can be found.on ticalc.org.
  
• About shells: There're many shells, but Doors CS by Kerm Martian should get most of your needs covered, as it provides compatibility with most mainstream shells/libraries.
  
• About bricking: It's nearly impossible to brick your calculator under normal operations, since TI has various protection against unintended FLASH writes, and as long as the Boot code(which is in protected FLASH regions) stays intact, you can always reinstall OS back into it. As long as you don't run suspicious 3rd-party assembly programs/FLASH application, and follow the instructions of software developers, your calculator should be safe.
  

The tips that I could give(based on my experiences) are:

• ALWAYS backup important data and programs! RAM is volatile memory and any bug in assembly programs could easily cause RAM resets and wipes your precious data away. You can put your data into non-volatile archive, or even onto another calculator/computer. Rebuilding programs that you've spent days from scratch is just a pain.
  
• Before asking something in the chat/forum, try searching in backlog/forum/Google to see if the problem that you have is already solved by others before.
  

That's basically all that I come up with at this moment. Welcome to Cemetech, and we hope you can enjoy your stay here!

Thanks for the advice!

I probably should've clarified a little more, but I'm already familiar with TI calculators in general. I have a TI-84+CE (which I use almost daily), and a TI-82. The CE is the faster 2018-present model, but I'm running OS 5.3.0 so I still have asm support (yay!).

I use my CE for academic purposes, and I'm mainly interested in using this for mucking with assembly and other nerdy and technical things, and some light gaming. It's good to know that I can mess with different OS versions with impunity, and that bricking isn't an issue unless I do something really stupid. I'll probably just run OS 2.43 if that's the best for software compatibility (MathPrint? Where we're going, we don't need any MathPrint!)

On the topic of on-calc software development, I noticed Axe and read some of the manual, and I'll probably give that a go. I hadn't heard of Mimas or CalcSys, and they appear to be a Z80 asm IDE and poke-around-inside-the-calculator tool respectively. I'll definitely try those out.

Are there any other progs that I might be interested in, in regards to the more nerdy-and-technical side of things?