The biggest looming question in my mind is, assuming that one day I complete a bachelor's sufficiently well enough to entitle me to the prospect of graduate study, would my first attempt at a bachelor's be too big of an obstacle to overcome?
My experience is of course anecdotal, but for me the answer was 'yes, it is possible to overcome a poor academic record in your first bachelors program'. I will outline my story briefly and then summarize a few takeaways.
I was a solid B student in high school, always doing well on exams but never taking homework very seriously. I overreached in my college applications and was rejected by five out of six schools. The one school to which I was accepted was the one I couldn't see myself attending, so I decided to enroll at the local community college instead.
I earned an associates degree with a ~3.5GPA and applied to three four-year schools, two for the linguistics major and one for the major in international agriculture. My associates degree was in social science, and I had been interested in linguistics since high school, but after working in coffee shops for a few years I was interested in the possibility of a career in the international coffee trade. I was accepted to all three programs, and chose to go to school for agriculture. My reasons for choosing that program over the linguistics programs still aren't very clear to me; in hindsight it was probably due largely to the fact that the agriculture program let me stay in my hometown while either linguistics program would have entailed a cross-country move. Regardless, I began at my new school and quickly got into academic trouble.
I didn't have the background for the courses I was enrolled in, I was still working full-time, I had an unhelpful advisor, I wasn't actually as interested in the subject as I had thought—any difficulty you name, it felt like I had to deal with it. I 'earned' a 1.0 GPA the first semester and a perfect 0.00 GPA the second semester, and withdrew voluntarily after that first year before the university could ask me to leave.
I got a full-time job and worked for two and a half years, but remained interested in linguistics and started to regret very strongly never entering a linguistics program. Finally fed up with myself, I applied to two schools: one of the two that had accepted me into the linguistics program three years prior, and one other. In spite of my poor showing in the agriculture program, I was accepted to both. I moved across the country to enroll in the program I should have enrolled in the first time they accepted me, and did very well there. I double-majored, earned my bachelors, applied to grad schools, and was accepted. I finished my masters degree this past May and am now in a PhD program.
So yes, it is possible. But...
I've learned a few things from my own experience. Take all of the following with a big grain of salt; they feel true to me, and they fit my experience, but they may not be generalizable:
Graduate schools are less concerned than you might think with your overall academic record and GPA. Rather, they are concerned with your ability to do graduate-level work in the program you've applied to. I had some terrible grades on my record, but they weren't in the subjects I hoped to study in graduate school. Over the entire graduate admissions process (I applied to five programs), no one asked about my poor grades from that year spent studying agriculture. It didn't come up once. That was very surprising.
I was honest about my academic record, but I didn't try to make excuses for it. I provided all of my transcripts, even the one with that perfect zero on it, to graduate admissions committees. However, beyond that, I didn't acknowledge those poor grades. There are people who will say that you should explain any poor grades in the statement of purpose you submit with your graduate application materials. I disagree. The statement of purpose provides you a maximum of two pages (in my field, at least; yours may vary) to sell yourself as a researcher. Any space you devote to an explanation of a poor academic record: 1) explicitly brings the reader's attention to a negative, and 2) leaves less space for other positives. The statement of purpose should give the impression that it's difficult to distill your research experience and potential down to two pages. If you don't even need two full pages, though, I think that's a negative.
The school in which I enrolled following that terrible year (academically speaking), from which I earned my bachelors, was one of the schools to which I had been accepted three years prior, before I had earned those low grades. I can't know for sure, but I can't help feeling like that fact worked in my favor.
What general advice would you have for me in my situation?
Are you in school again now? If so, you've already cleared one big hurdle. Regardless, my advice is pretty simple: do everything you can to demonstrate that you can perform at the graduate level.
Take challenging courses—I was able to take a graduate course during my last semester (which took special permission from the professor and the college) and it was hugely helpful to have an idea of the expected workload.
Make sure your writing sample is the best it can be. A strong writing sample can go a long way in the admissions process.
Don't make excuses for yourself, but demonstrate through your recent work that any past poor performance doesn't reflect your real potential. In my own experience this was not as difficult as it might have been: I earned decent grades in social science, poor grades in agriculture, and then good grades in linguistics. I expect that poor grades and then good grades in the same subject might cause more concern.
Recognize that in many ways your extra lived experience (compared to your academic peers) is a strength. Many people go straight from high school to college and then straight from college to graduate school. Your experience working odd jobs and saving money for an out-of-state move might not be academic work, but it might give you a maturity and perspective lacking in other students. Compared to someone who's never taken time off from school, you might have a better idea what you want to do with your life.