I put in a wood-burning fireplace a couple years ago. I started with zero knowledge on the topic and felt pretty confident in the end... at least with that singular process for that fireplace. I found the installation manual to be completely packed with specific information that made me confident in doing it entirely myself. My fireplace uses a double-wall stainless flue that goes through the roof without any chase or enclosure. It is even a snap-fit assembly. Super easy. I just had to maintain X inches away from anything flammable. I'm even a terrible roofer and I had no problems taking a sawzall to my roof.
You'll find these days that many manufacturers do their own proprietary flue system. The days of randomly putting a 6" stove pipe on anything are mostly gone unless you buy a vintage stove. Then the difference becomes pretty clear. Think of it like the difference between buying an IKEA desk with special instructions that you can confidently assemble in 30 minutes versus starting with a tree that you mill into lumber and construct your own desk. The newer, proprietary stove stuff is a complete IKEA package. The older stoves you have to know what you're doing.
I found two companies very handy. efireplacestore.com and woodlanddirect.com. I ended up going with one over the other, but I forget which. I think I went with Woodland because their customer service was great. They were always willing to answer the phone and listen to my dumb-ass questions. Of the three local sales/installation places I visited, they were all like a used car lot. They were very tight-lipped about information and they wouldn't even quote me on anything other than the entire job.
One word of advice. Don't get the cheap stove. I bought an entry-level fireplace because it was so much cheaper than the fancy ones. It was also one of the only models that came in a small enough size for my tiny house. Until I spent the money on the flue, the stone facing, the hardie backer, the roofing products, etc (some of which you won't need) I ended up totally eclipsing the overall budget. I felt like I bought the cheapest brake pads and then invested in a good car to install them on. It just ended up being a dumb place to save money.
Another thought: call your home insurance company and ask about if/how it will change your premiums. Strangely, in my case, the open fireplace they had zero cares about. They didn't even need to know that I was doing it. If it had doors with a seal (like a stove) they would have raised my rates a small amount.
Last thought: Dig through your municipality's rules to see if you need a permit. I was advised by some builders that yes I technically needed one, but it's too much of a headache and I run the risk of being denied. I did anyway, it was approved, and the inspection was literally a guy walking in and saying "yup, it's a fireplace." YMMV.
OK... really my last thought: Don't forget to add CO detectors. They're cheap and a lot of the new 10-year smoke detectors come with CO detection in them. If you're adding a chunk of pyro in your house, it probably wouldn't hurt to upgrade detectors anyway.
If you want to go the GRW route (grassroots woodstove), I would imagine you can find a used stove that takes some random stove pipe and just start your learning curve.