Shouldn't be too hard. I got back into cycling on a mountain bike about 10 years after college, then decided I wanted to ride the road, too, but couldn't afford a bike. I even did a couple of metric centuries on an old Bridgestone MB3 with just a tire swap
I never could feel much difference among MB road tires--the worst is better than a knobby tire. I haven't shopped at Performance in years, but I used to, and I was always satisfied with the house brand stuff. You're wise to stick with 1.5 or so, too, if you weigh more than about 140.
whether wheel wobble matters depends on how bad it is, but it's usually fairly easy to adjust out. Google "truing a bicycle wheel" and you'll get more information than you can stand.
No reason to change the bars if you like what you have. You won't have as many hand positions as on drop bars, but my wife has ridden 3000 miles this summer with flat bars. I also wouldn't worry about the gearing. Most people have far higher gears than they need. If you reach a point where you're pedaling as fast as you can in your highest gear and still want more, worry about it then. It won't happen soon.
Re the fork: I don't know anything about that particular one, but taking it apart, cleaning it and greasing it can't hurt. Type of grease probably doesn't matter much--loads on bikes are fairly low, and any decent slippery stuff should work. You may be able to download a manual, or at least tips, for the thing. I did that recently for a 14-year-old Rock Shox Q21R.
Before you pay for a tune-up, try cleaning and lubricating every pivot point on the derailleur, then loosen the bolt that holds the cable to the derailleur, pull out the cable (from the shifter end), smear it good with any kind of grease and run the cable back through the housing (or replace the cable--they only cost a couple of dollars). Google can help you here, too ("adjust rear derailleur" is a start). Also lube any place the cable slides against something, like maybe under the bottom bracket. Use a LITTLE lube anyplace that's exposed to dirt, and wipe it off after a few minutes. Lubricate the chain as well, and for that, a bike-specific chain lube like White Lightning or ProLink is worth the money. Ordinary oil will work, but holds dirt like you wouldn't believe.
Rust spots on the gears is pretty much harmless. Spray the cassette with WD40 or something, let it sit a few minutes, then use an old towel or rag to get between the cogs, like flossing teeth. It doesn't need to be lubricated, by the way--you're using the WD40 as a cleaner and solvent and wiping it off
Other things you may need: Tubes, rim strips, brake pads. And of course tools, which you can buy as the need arises. Bikes are simple; anybody can learn to work on them.
All this information is widely available online. Try www.parktool.com or www.sheldonbrown.com.