So, what I want some help with is this: if I go back to school for a second bachelor's degree, what sorts of programs should I look for? I know some (usually for-profit) schools have programs that are explicitly about "video game design". But assuming a given college or university I'm looking at doesn't have an "video game design and development" program, what should I be looking for?
Unless the two schools you are considering are named "UCLA" or "DigiPen" (or maybe a few others ...) I would advise you to ignore game development programs. Instead, figure out what discipline you want to pursue, whether it be concept art, game design, audio, programming, quality assurance, production, etc. For what it's worth, having a relevant degree really only helps with two of the above roles. As an example, if you really want to be a video game artist, start drawing (or modeling/animating). Throw something up on ArtStation or DeviantArt. Nearly every artist I've worked with has regretted going to art school (largely a waste of time) but if art school is a means of providing structure to force you to sit and draw, then by all means go for it.
On the Big Studio vs. Indie route: Probably go for the big studio, even though I'm old enough (34) that they'll probably just write me off anyway (tech in general and video games in particular have a bad reputation for ageism). Thing is, in order to pull of an Isaac or something, you need to have a pretty specific idea in mind. I don't. I'm generally better at helping to bring an existing idea to fruition (as a musician I was a classical and operatic singer, so I wasn't writing my own material). Plus, I dunno, I'm middle-aged enough that I value the stability a larger firm would grant.
Surprisingly, video games actually has a reverse ageism problem. The problem with entering the games industry is that most jobs have a <shipped X titles> or <N years of industry experience> requirement. "Entry-level" is virtually nonexistent outside of companies that have setup explicit programs for it (e.g. Blizzard or Epic). You may be surprised to discover that many game developers fall in the 30+ with kids bracket, mainly because of the hostile barrier to entry. From what you've described so far, I suspect you would rather enjoy being a producer.
As for what to do in the process... *probably* programming. Or level design or similar. But I do want to explore some of the 3D modeling and graphics as well. But, I think initially focus on the programming part and branch out from there later if I'm so inclined. So let's say programming.
Depending on the size and composition of studio, programming basically has nothing to do with level design, modeling, or graphics (unless you are explicitly a tools programmer, a technical artist, or a graphics programmer respectively). In the particular case of game programming, you have to really love game programming to go into game programming -- this response is getting a bit long already, so I'll skip over this part, but just ... be forewarned. It's a radically different beast compared to other programming jobs.
Check the art department to see if they have a digital art program, it might be where all the video game designers opted to go. Similarly, check the computer science department, they might have people who are majoring in CS with a focus on game design or a minor in game design.
This is nominally good advice, especially if you're interested in going indie. I'll also add that most game designers I know started in QA and worked their way up after roughly five to seven years in the trenches. The art and CS departments are a good place to find people who have the inclination to go indie, and are less elitist (for lack of a better term) about the people they want to work with. If you have a few (shipped) indie titles under your belt, it becomes easier to make the jump to professional (AA or AAA level work).
Most games aren't made with C+ or C++ nowadays.
You're not likely going to get much from a big company. Not because of your age but because of inexperience and they're very competitive.
Practically every PC/console game is (still) made with C/C++ these days, sometimes coupled with a scripting layer on top (Lua, Blueprints, Flowgraph, etc.). It's just not immediately obvious that this is the case.
Big companies have a deep focus on specialization. This isn't to say you aren't going to get much. It just changes what you get out of it. For instance, if your goal is to gain a deep understanding of <Insert Advanced Graphics Technique Here> using <Advanced Rendering Technology> ... that's not something you're likely to get at an indie shop.
In closing, the first question you need to answer before anything else: "do you want to make games for money?"
There are many ways into the games industry. If you want the freedom to make indie games as art, that's great. Just understand you are unlikely to make millions doing so. On the other hand, you might have a lot of fun working in a large studio where you get paid slightly more money at the cost of relinquishing creative control. Sometimes you get lucky and end up with the best of both worlds, or you might not. It helps to know where on the scale you fall though. :smallsmile: