What are the main things to upgrade on a bike? What would you recommend be upgraded first in order of importance?
Hard to say, the bike will dictate that!
Like NT says, regular maintenance is a good thing, and checking for wear and tear. A slightly loose bolt will wiggle, wearing away at the nut, or the bit it's bolted through, making itself worse.
You could start by giving your bike a really good over all health check - think of the letter M.
If it's possible, get the bike lifted up off the floor - easier on your back, and lets the wheels turn.
Start at the front wheel. Check for loose spokes - squeeze them in pairs to feel how tight they are. Turn the wheel by hand, look for wobbles. Grasp it by each side of the rim and try to wobble it on the hub, to check for loose bearings there. Then go up to the headset. Can the whole fork/handlebar set move in any dimension other than the way it should (to steer)? Check all the stuff fitted on the handlebars - gear shifters, brake levers etc. Are all the bolts done up properly? Do any bits wobble even when everything is tight?
Then down, to the bottom bracket and pedals. Same things, does anything wobble in a direction except the way it should move, and are all bolts tight. Grasp the pedals and see if they'll rock to and fro, may indicate bottom bracket wear.
Then up again, to the saddle - you've already had a go here - bolts all tight, so unwanted wiggling.
And finally, down to the back wheel. Same checks as the front, plus checking over the gear mechanism.
If you're keen, you could use the opportunity to clean everything as well, get any gunk out of the cogs etc. And while you're at it, follow the lines of the cables and see what happens at the business end when you pull the lever. It'll all help you understand HOW it all works, which makes fixing it easier.
If you find a bolt that's loose, tighten it gently. If it does't seem to be curing it, don't overdo the force, think about replacing the blot. When doing any reassembly, use a little grease on the thread to prevent it rusting up and being impossible to get off next time.
There are lots of books out there that show you how to do basic takes, and some more complex ones. But the internet is free, and often you can target your searches to just the jobs you need, without getting pages on jobs you'll never need to tackle.
The main thing is, don't get too worried. Bikes can actually go on and on, it's not ideal but they can take a lot of punishment. Try and keep it relatively clean around the chain, give it a good look over everyso often, and it'll probably serve you well.