Like the title says, I don't have any issues right now, just some general questions.

I am newly back to biking, so I am a beginner at bike maintenance. As a teen I rode seriously, but I'm turning 50 this summer so that was some time ago. My previous adult bikes, I simply had the bike shop take care of the bike for me. Well, I didn't ride much (I was quite fat for years, but I'm losing weight, down 75-80 LBS since Sept, so that will change), and it still got expensive. So, when recently buying a new bike, one of my goals is to learn to maintain my own bike. When I got it, I thought the seat was way too high, but instead of having them change it, I did it myself (simple job, and after watching some You Tube videos and reading about saddle height, I now know I need to move it back up a bit, though not as high as when I picked up the bike). On my first ride, I was having issues with shifting, I couldn't get it into the lowest gear for going up hills, but with a few You Tube videos and a little reading, adjusting the derailleur was a snap (there are a few hills around here where I need the lowest gear for part of the hill).

So, for my questions...

First, how much should I do as a beginner? I'm only semi-competent with tools, I'm far from a handyman, but I can do basic maintenance around my rental home, and I changed the oil on my motorcycle once (with the placement of the oil filter, and many scuffed knuckles, I decided after that once that it was worth paying to have it done). After a year or two with my bike (a Giant Escape 2), I'll probably want to start upgrading components. Which ones should be relatively safe for me to do (safe both from an actual safety standpoint, and also from the standpoint of not totally messing it up and making the fix far more expensive than taking it to a bike mechanic for the work to begin with)? I do have a friend (a co-worker) who is also a bike mechanic, but since that is his part-time paid gig, and his former career, I don't want to take too much advantage of him, but I can get my mistakes fixed relatively inexpensively.

Next, what is done in the typical yearly tune up?

Finally, what tools do I need? Right now I have a decent basic tool kit, but anything bicycle specific that I need?

Metric combo and Allen wrench sets are a good start: combo wrenches from 8mm to 17 or 19mm, 4, 5, 6mm Allen wrenches and perhaps 7 or 8mm depending on your bike. Bike-specific tools depend on your specific bike and what components it has. Tools for servicing freewheel or cassette, hubs, crank, and headset will depend on what you have.

Park tool has general information as how often to do certain maintenance and specific info on adjusting and repairing different parts. Most repairs are not difficult and can be easily learned.

1. Think about how you want to clean your chain. One of those hidden link chain pliers is worth having in your kit. At some point you'll want to replace a chain and need a chain tool to shorten it.
2. Almost anything you do to a derailleur or brake is going to result in a frayed cable. When the day comes that you decide to buy a cable cutter, step up and buy a good one.

I have never regretted the money I spent on my Felco cable cutters decades ago; they still work like new. If you buy quality tools your work will go better, and you will be able to leave them to your grandchildren.
In my opinion multitools suck. If you try to mount a water bottle cage with a multitool you will see what I mean.
Get a good set of hex L- or T-wrenches and combination wrenches. l like Bondhus L-wrenches with a ball tip on the long end for angle work and a standard tip on the short one for high-torque use.

A decent, low end bike work-stand will set you back $50 or less, and provided you have room for it, will make you a much better mechanic. My road bike lives on the work-stand when I'm not riding it. Sure does make it easier to tweak those shifting, braking etc. issues with minimal frustration and self-contortion. Great for cleaning rim braking surfaces and lubing chains too.

Get good at routine adjustments to shifting and brakes. And flat tire repair. I volunteer at a non-profit and most of our donations come in with shifting problems, worn brakes, and flat tires. Most of this needs little more than a set of Allen and combination wrenches.

If you cycle a lot of miles, you'll be replacing the chain and rebuilding bearings every year. You can gather tools as you go. Some of those will be bike-specific.

As far as safety goes, be extra careful when working on brakes. If possible have someone check your work after you replace components. I'd rather have a shifting failure than a brake failure.

Another safety issue is front wheel and steering work. Don't compromise the fork, stem or bars.

For personal protection while working, always wear eye protection if you're shaping metal (more advanced work). Think about where your fist will hit if and when the wrench slips. Use the large muscles in your upper body rather then your wrists and keep control of the tools. Generally this much torque is only needed on the cranks.

I find my 11 speed shimano 105 needs adjusting once or twice a year to keep everything piss perfect. That's all the maintenance it needs other than changing tires and tubes.

If you only have one bike to work on, then doing other things like replace bottom brackets, changing cables and housings and even changing chains are going to be many years down the road. So I wouldn't stock pile tools until you need them. You might find the tools you use to remove something won't be the tools to put a new model on with.

You said you got a new bike I think.... did you take it back for that free tune up they may have mentioned? Around here that would be a decent check and adjustment of the shifters/derailleurs. Also a check of the brake and wheels with spoke tensioning and truing if needed. Sure you can do that yourself, but if the bikes new and still in warranty, now isn't the time to be completely DIY.

I just picked it up a couple days ago, so not yet, but I will. As long as it is free I'll have them do anything that will take more than the hour drive and back. I did the couple little things it needed when I got home because I wanted to learn anyway (for the derailleur, the saddle is simple and took no new learning, in fact, I even set the right height which I thought I might not have once I started watching YouTube), and it would be quicker than the drive.

I don’t know about your relationship with the shop, in fact this might be a good time to start one. If you can find a time when they are not too busy, ask if you could watch while the tech checks out the bike. A chatty tech could teach you a lot. Good luck.

#2 just isn't true. It is quite easy to adjust or remove a brake or deraileur without damaging the cable
For general maintenance Allen keys tyre levers and some screwdrivers will get you by..

If there's a bike co-op in your area, you can get help with maintenance tasks and learn by doing with an experienced guide.

I'm sorry. I'm pressed for time tonight and admit that I didn't read through all the previous responses, but I'm sure someone must have commented by now that there's sort of a built-in gauge for deciding which bike repairs you can do on your own and which are better left to a bike shop. As the repairs/maintenance procedures get more complicated, the tools to do them get more expensive. When you reach the point where you have to buy a $50 tool to do a job your bike shop will charge $75 for, you have to make decisions about how much your own satisfaction in doing the job yourself is worth.

I have always liked learning new things, so my tool collection has gotten pretty large and expensive and the work I do on my own bike has increased. The problem with this is that I am no longer on a first-name basis with all the bike mechanics in the area, so when I do need something tricky done, I don't have go-to-guy I can trust anymore.

It's always a trade-off. No rules here.