Try this out, this is the book that started our building company's owners on the right track. Feel free to message us directly, we have done several basement remodels!
You need to insulate your walls. You can get an R-5 insulation board that’s 1” thick at any big box store. You can glue or screw this to the wall. Your walls are very unlikely to be flat and straight so you’ll end up with a gap either way behind the studs. You’ll fill between the studs with fiberglass or other insulation after your inspection.
Honestly, the ceiling in my basement is a couple inches shy of 8” and it doesn’t feel low. I’d highly recommend finishing it with drywall. I’d also recommend hiring out the drywall. Literally everyone I talked to said hire it out. It cost me around $4k for 600 sq ft and seeing them do it made me realize it was 100% worth it.
You’re probably going to want to pick up a book and watch some YouTube before you get too far. I’d recommend the Home RenoVision DIY channel on YouTube and this book Remodeling a Basement: Revised Edition (Taunton's Build Like a Pro) https://www.amazon.com/dp/1600852920/ref=cm_sw_r_cp_api_i_15PSF7RZNDCVKMTC092S.
Visit your local building department, and pull permits for structure, plumbing, electrical, insulation and drywall (if needed). Do this correctly and you will raise the value of your new place by tens of thousands of dollars.
Then hit Youtube, and perhaps purchase some books:
https://www.amazon.com/Remodeling-Basement-Expert-Advice-Tauntons/dp/1600852920
https://www.amazon.com/Complete-Basements-Stanley/dp/0696227428
https://www.amazon.com/Black-Decker-Complete-Finishing-Basements/dp/1591865883
https://www.thisoldhouse.com/basements/21017847/read-this-before-you-finish-your-basement
Done this, it's a LOOONG project.
I liked this book for reference: https://www.amazon.com/Remodeling-Basement-Revised-Tauntons-Build/dp/1600852920
Youtube is also good but it's nice to have a trusted reference as well because there are some crazies on youtube.
The first step is drying out your basement. Make sure you have gutters, that they are in good working order, and the dirt around your house flows the water away from the foundation. Also clean your window wells out and make sure they drain. I had some that would fill with snow then leak into the house.
I would hire the sheetrock done by pro's. Most tasks can be thought out and done with some mental effort. Sheetrock really takes practice and muscle memory to be good at. It's also miserable hard work that will take forever.
Get acquainted with your local codes, usually the city offices have cheat sheets for everything you need. There may be a few surprises, but if the inspectors can tell that you read the instructions they are easier to deal with. Also you can call and ask them questions on how to do the job right. When you think of it, the inspection fees are a great deal because a pro comes out and makes sure it's right and answers all your questions.
Take your paint prep seriously. Wire brushing, washing, then acid washing the concrete walls is important. Consider painting your floors to seal them, I think it makes everything go easier, and the basement smell better.
Wire up your lights as soon as you can, it makes the work easier if you can see well.
I liked using the plastic Ceiling Max ceiling tile system. It's tedious to put up, and MUCH easier with 2 people. The tiles smell a little like natural gas when the box is first opened, which made me think I had a leak for about a hour, but that was the biggest issue. https://www.youtube.com/watch?v=Sqvbr7O80Og
For flooring I'm a big fan of the Allure Vinyl Planks. They are similar to the click together floors, but they have 2 self adhesive sides that hold them together really well. This makes them more tolerant of imperfections and slopes common in basement floors. https://www.thespruce.com/vinyl-plank-allure-flooring-1824803
I tend to get these at Home Depot, but the in stock varieties are pretty meh so consider planning ahead and ordering something.