If you're looking at going this route I can make a few suggestions. I did something similar.*
First, off, the breakdown is something like: just take classes as a post-baccalaureate, either towards a degree or not / go to grad school (and if you do go to grad school a PhD program is more likely to be funded, even if you leave early with a masters. Do not pay for a stem PhD yourself. It's wrong.)
So, when I started looking into heading back, possibly to grad school, I did two things: First, I contacted a few potential programs, and talked to their admins, and got an idea what they were looking for. I thought I'd be a hard sell, they were mostly all "You can code? You should apply right now. Or really soon." But I still got them to give me a list of useful classes to take - I had a bunch of money from stock options and wasn't I liked research. And I started taking a few classes.
Next, I started looking for a lab where I could volunteer and get research experience. There are also paid positions, obviously I was in a super privileged place here. Again, I expected this to be hard, and instead something like 3/4 of the PIs I met were all "And if you come work for me, this is the desk I'd like to chain you to." Generally, paid work is, well, paid. Volunteer work is easier to get and more likely to be entertaining. I ended up spending a couple of years in that lab I picked, ended up running a project with grad students and post docs reporting to me, and got my first first-name publication out of it. Oh, and wrote and got my first grant funded. (Okay, I'm told this whole experience is a little non-standard. But hey, things like this do happen.)
Eventually I got around to applying for grad school. And by then, getting in was super easy. (Okay, I was wait listed at one place :-( ) But, y'know grad school is all about having serious research experience, far more than it is about having the right classes. So good letters of recommendation from people who knew me as a researcher and a publication history was just golden. Also, by that time I'd acquired a lot of the right classes. (Enough so that I got excused from the required first semester classes for my grad program.)
So... okay, I realize not all of this is replicable, but a lot of the parts are. It is easy to get research experience. (I spend a lot of time helping folks find labs to volunteer in - the ones who aren't working for me already, I mean.) I mean, it takes persistance, but it's not like it takes talent. I recommend contacting PI and asking if you can sit in on lab meetings - this is a pretty much no commitment thing for them, so they're a lot less likely to blow you off.
Similarly, you can just call grad programs, and the people there will be happy to talk to you, and you can start figuring out what you need to do to make yourself a viable candidate. (Of course, once you get research experience, you'll also get the inside scoop, which is often substantially different from the outside scoop.)
Finding research related jobs - again, more persistance than talent. Check out the online boards, but also show up on campus in person, as some things just get announced via a piece of paper. Talk to folks. Ask around. Think about how you can use the skills you already have.
And if you can't code already? Go up to Python.org and start working through their tutorials. Really. Python loves you and wants you to be happy (this was more or less the motto of the summer python club a few of my students twisted my arm in to running. Well... really, they ran it, I just showed up and had skills.)
(and if you want to talk about any of this, happy to chat)
* Sort of. I did my undergrad work in Chinese and PoliEcon, then worked as a software engineer. Then I went back to see if I liked research - hey, guess what? Research is awesome, at least if you're broken in the specific ways I am. So, substantially different goals, but some overlap of potential approach.