Unfortunately, as far as I can tell all dental insurance is pretty lame. Every policy I've had for the last several years maxes out at $1500 annually, and some have a lifetime max that isn't much higher. So don't feel bad about not being insured; it honestly wouldn't help that much.
As far as having the extractions goes, I just had mine done three weeks ago at a place that specializes in it. Yes, I got an immediate denture. I'm only 40, and the thought of walking around toothless was not okay with me.

Before that I had years of problems because of an autoimmune disorder (essentially I have very little saliva, which has caused lots of dental problems).
I am going to get implants, but if I weren't, the course of treatment would go something like this: extractions, immediate denture that day. A few checkups over the following two weeks. Soft liner at about two weeks post-op to make them fit better. New soft liners as needed until several months down the road, when you're all healed up and ready for your permanent denture which should not need a soft liner. (My SIL works at the place I went and explained it to me.)
Now, I am going to have dentures for several months before my bone is ready for the implants (I had bone grafts), and I won't lie. It's been challenging. The lower plate especially is annoying because it likes to pop up when I try to eat. However, I have a small mouth, not very deep gums in the first place, and then I had a lot of bone loss, so other people might have it easier than I do. Also I might be pushing it as far as eating is concerned. Probably I should stick with the softer stuff for a while ... but dang, you get sick of pudding, ya know?
But the pros: first, I have a prettier smile. No, I have a
pretty smile. Even when I was young and my teeth were in good condition, they were kind of crooked and a bit yellow, with an uncorrected overbite, so I always felt a bit self-conscious about them. When they started decaying, I felt
really self-conscious about them. I haven't truly smiled in a photo in years. I'm kind of in love with my smile now. Even though it still looks a bit funny because of swelling and the soft liner and the fact that they set the teeth a bit low in the denture (which will be corrected in a few months) ... even then, this is still the nicest my smile has ever looked.
Second, the pain. Basically, there wasn't much at all! I did take the prescription ibuprofen they gave me for inflammation, but I didn't even get the narcotic script filled. Never needed it. And my mouth was in pretty bad shape, with lots of abscesses. Gentle salt-water rinses nightly and this stuff called Sock-It (I think) which numbed the gums were all that was required. They did miss a root tip and had to go back in to get it a week or so later, and that hurt a bit more (during healing; you can't feel a darn thing during extractions because you're so numbed up), but mainly because that sucker was hanging on for dear life and the dentist had to yank a bit.
Third: I don't have to worry about what I'm going to do about my teeth anymore. I already know. It's such a weight off. I was also worried about what my bad teeth were doing to my general health, and now I don't have that worry.
I can't give a huge amount of advice because I'm so new at this myself, but I just wanted to let you know that even though the first few weeks after dentures is challenging and can be a little disheartening—they feel so weird at first!—it gets a little bit better every day. And it's way way better than what you're going through now.
Also I just wanted you to know that I have heard of lots and lots of women losing teeth during pregnancies. It's because of the extra calcium required at that time, I believe. You're SO not alone.