Is this a big deal?
No, there are plenty of people on here to help.
I'm thinking of doing it. I'm not concerned about operating the machine itself, but I don't know a damn thing about the "logistics".
Will I have to buy a different wireless router? Will my ancient Telus modem (don't ask, I have both) connect right to the machine and work?
No new router. Don't know about Telus setup.
Will peripherals that I currently use (printer, second monitor, wireless keyboard and mouse, speakers) plug right in?
Yes, except the keyboard and mouse which will probably work. Like 99% chance.
It will be a laptop, but it will spend most of its time as a "workstation" here on the regular desk and I hope to just take all my stuff that's connected to my PC and connect it to the new gadget.
Mine is the same except my desk is a couch.
I am a stupid, impatient "man" and I will be making the switch reluctantly. If it takes several hours (or, heaven forbid, days) to straighten everything out, I'll just stick with the PC sitting under my desk and continue being the fatter guy in the commercials.
I've been a Mac user damn near 20 years and I am still straitening things out. 
Don't get to the point where you are frustrated with something, just ask.
Most importantly, I want to spend as little time on the phone with my ISP provider. I'm sure I'll have to spend some time with them, but the littler the betterer.
You should just have to add the new MAC address but I don't know for sure. If you had Shaw, you just plug it in. I can't imagine Telus would be that much different.