First of all, welcome to HLP, and congratulations on discovering FS2

There's a reason it made that list, and that reason is that it's quite possibly the best spacesim ever made. So if the genre is to your liking you've got something to look forward to.
As for your questions, lets take them in order:
The main Freespace campaign is where you should start if you want to play in order. After that Silent Threat, and finally the Freespace 2 campaign. Be aware though that Silent Threat (an expansion to FS1) was rather rushed and buggy, so it may be a bit frustrating at times - Fortunately the two true main campaigns do not suffer from this. Awakenings is a fan-made campaign and as such does not figure into the official timeline, meaning you can pretty much play it whenever you like, though I'd personally wait at least until after finishing the FS1 campaign.
As for buttons, it's hard to say what is 'optimal' as this will inevitably vary with personal preference. Also, you should know that since FS2 is a rather dated game by now (though with vastly upgraded visuals due to the efforts taking place here), it does not support all the functions and buttons available on modern joysticks. I know it supports up to 4 buttons, a 4-way hat switch and a throttle for sure, but above that, no guarentees. This will change eventually with the code upgrades underway, but for now, what you get is what you get.
So anyway, here is the setup tend I use for SP games:
Button 1 - Fire primary (guns)
Button 2 - Fire secondary (missiles)
Button 3 - Target nearest hostile
Button 4 - Launch countermeasure
Hat Forward - Target object in reticle
Hat left/right - View left/right
Hat backwards - Transfer energy from weapons to shields
I sometimes think about mapping afterburners to a joystick button since I tend to miss the tab key when I'm panicking, and I've also sometimes had left/right-hat mapped to rolling, so that might be worth experimenting with also. But above all, experiment, and find something that suits you - Especially as I've been told before that my setup is downright weird

I guess that about covers it. Enjoy your stay, and don't be afraid to ask if anything else comes up - We aim to please
