I have a 30 year old car and there are one or two specialists in my city that people recommend. One of them told me I needed an engine rebuild due to an oil leak, when it was actually a specific seal that was relatively minor to replace, and the other correctly diagnosed the problem, and apparently fixed it for a reasonable price, but insisted the oil I was using was too thin, and when I deferred to their expertise, they put an even thinner oil in (I found out later) and lied about it...maybe because they thought I would come back with more leaks...so the only local mechanic I currently trust is a dealer that will work on classic cars and they charge a ridiculous amount.
So, comparing cost and expertise and tools is kind of missing the point. I would always take a new or newish car to a dealer. I have no idea how to find a decent independent mechanic, and I've tried quite a few over the years. If it takes me several times as long to do something, it doesn't really matter if that's my only practical way to get it done right.
It really depends on what service you plan to do. If you're going to do things like changing bulbs, air and cabin filter, wipers, and the battery, you could get along with just a conventional socket set if that.
Oil changes will require a oil filter wrench/cap, a torque wrench, and a funnel. And those tools can also be used for transmission fluid changes.
Once you get to spark plugs and brakes, you'll need more tools, but those services aren't frequent enough to really warrant buying the tools as opposed to renting them.
> takes a bunch of time
I typically will change the oil on my vehicles myself and a oil and filter change takes me about 45 minutes (including the time to drive to the auto parts store to recycle the old oil). The last time I took my car somewhere for an oil change, I had to drive to 5 different places and finally had to settle on one that made me wait about 3 hours before they could get to it and change the oil.
There are certain services or repairs that will take time (brakes, suspension, exhaust) where I would just as well take it to a mechanic to do it for me, but there are plenty of others that don't take much time at all and cost significantly less in terms of saving on labor and your time for setting up an appointment, taking the car there, getting alternative transportation or waiting, getting the car back, etc.
If you genuinely enjoy the process, and it is cathartic and serves the function free time and leisure needs to in your life, then fantastic. But otherwise it's a false economy.