From reading the SS car thread alone, now is not the time you want to be buying a car and the inflation on new and used cars has probably outpaced the inflation on parts and service.
For any work under the car you need a jack and at least 2 jack stands. Never get under a car unless it has jack stands. Look up "jack stand positions" or "jacking points" for your car to find out the best place to put them. Ideally, also put a brick in front and behind the tires that are still on the ground, as well (or get tire chocks).
For doing the brakes yourself, you will probably want a socket wrench set, an extender for said sockets and a cheater bar, or at least some penetrating oil to break free the old bolts (also, you may need metric and standard sockets). Harbor Freight tools are probably sufficient for rarely used tools.
Rotors can wear out, and on 100k+ miles, they are probably correct on needing to be replaced. You can probably find a video on how to evaluate if your rotors are bad, just by looking at them (the brake pads will eventually cut deep groves into the rotors). Brake pads can be done alone, but you want to replace both when rotors are bad.
Look up how to change brakes and rotors for your car type on Youtube and there should be a tutorial with in +- 5 years. It's not as easy as changing the oil, but then, if you follow a tutorial on how to keep air out of the brakes, it isn't too hard.
Replacing a control arm and it's bushing (where it connects to the frame) may be more involved still. Youtube is your best friend on evaluating if you think you can tackle such a project and what tools are required. Also, I would assume they meant both front control arms plus their respective bushings (when it comes to suspension, you usually want to do both sides at the same time anyway).
There are a decent amount of users living in Texas, especially the DFW area, so if you list a close city (if you're in a major metro, it would be Plano, Woodlands, Georgetown, White Settlement, Humble, etc.) or side of town, someone might have a recommendation for a "trustworthy" mechanic (if they happen to read this thread).
Here is the best picture I could find showcasing the grove the brake pad cuts into the rotor. An official test used a caliper to measure the thickness and compares that with safety guidelines.