First, my acknowledgement and thanks to you all for your suggestions and constructive support. I appreciate the can-do and positive attitude towards these potential obstacles that I see on this forum, and it's part of what compelled me to put this up here.
It's definitely the truth that I do struggle sometimes with this kind of change. I have been thinking about owning a place for years, and in my mind I had a certain expectation of the work and kinds of effort I would be putting into it. As things have come to pass, I'm recognizing a certain sense of disappointment and letdown around the fact that my expectations don't line up with reality at this moment. That's okay, but there's definitely an emotional response that I have to work with to really accept. These life changing events become a flash point for the anxiety I carry around with me from day to day. I have to learn to recognize that and keep my brain in order.
Thinking about this from another angle, I'm very fortunate to be in the position that I am of being able to buy a place. I'm fortunate to actually have the cash on hand to deal with these problems. My 20s were spent toiling in a profession where I was earning very little and constantly struggling with anxiety and burnout - my anxiety level was so high that I even passed out on a couple occasions. I'm now in a different career where I earn a decent income, feel generally competent at my work, and am valued as a contributor for both my skills and insight. This is what has even put me in a position to be able to buy a place, and long after the scarier issues are resolved, I'll still be earning a decent income and hopefully have a nice place as well.
Going into this, I chose the place I did because it seemed like a well-enough maintained property: old, but in decent shape. I was willing to spend more on a house, but wanted one I could make my own. This one (at 100K) is significantly less than I was ready to spend. My hope was to put in around 15K, live here for a few years, and then either sell or rent it as I moved towards something that I liked even better (my tastes run modern). After speaking with a chimney sweep today, it's seeming more and more like 15K is a pipe-dream. In addition to finding out the gas inserts upstairs contain asbestos, it turns out the furnace flue is unlined. I'm looking at 2-2.5K to handle the four fireplaces and line the flue.
I appreciate everyone's advice to deal with the safety issues first: no repair bill is going to be as bad as a health issue or attorney's fees. I am in agreement with you all on this, and just need to figure out how to prioritize those: the asbestos tile is basically good shape, and could be covered up. Removal probably wouldn't even be financially onerous. I'm less confident about the plaster issue - I can't imagine every house that has asbestos in the plaster gets abated and replaced walls? I'd guess that the 1920s art-deco building I lived in down in florida had asbestos, as did the 1930s townhouse I rented, as does the 1950s apartment complex I currently live in.
I have partial knob and tube wiring, and partial romex. The panel is a fuse box. The electrician I met with yesterday said that he would suggest leaving the K+T in place, as there's no insulation covering it and it's only powering the lights. Another electrician suggested I that using LEDs would further reduce the issue as they would place less draw on the circuits. All agree that the outlets in the kitchen and bath really need to be switched out to GFCI.
The lead paint issue is a concern, but I'm confident that with good protection (purple filters, booties, lots of plastic, that soy-based stripper) I can mitigate where necessary. Most has been covered up already and the windows were replaced so it's not an issue there. Mainly the closets and doors need some attention, as they are either uncovered or some abrasion is happening.
I suppose really the question is what do I need to do to make this a safe place to live, and then how to prioritize getting those things taken care of. After that, I can begin to make some improvements along the way (and hopefully not feel like I'm endangering myself and anyone who comes to visit me).
I'm fortunate to be in a position where I can afford to do this without feeling like I'm going to go broke. I have ~8K in cash that I can comfortably spend on this (I want to make sure I have at least 20K for a real emergency), and then another 15-17K in stocks I was originally planning to liquidate when I was looking at buying a more expensive property (I have more stocks than that, but I don't want to end up house-poor!). I'm also fortunate to have a resource like this forum, with creative and positive-minded folks who think outside the box and have some experience in these matters.