Relays are everywhere. You don't need to spend $30 on one either.
I bought a 5-pack of 5v relays for about $3.50 last year, so less than $1 each. The only drawback was most of the writing was in Chinese. Fortunately my multimeter serves as an effective language translation tool.
Find an old USB 2.0 cable and cut the other end off. Find the red (5v) and black (GND) wires. You won't need the green/white wires.
You only need the more common low-active relay, which is what I used (high is fine too, but instructions slightly different). On one end there will be 3 terminals for Vcc (5v), GND and IN. Vcc and GND are self-explanatory. For IN, just jumper it to the GND terminal with a short piece of wire.
First, the relay must be getting some power (a few milliamps) to become active. So turn on the Pi. Then, because GND is connected to IN and it is low-active, this will trigger the relay. Because my relays have Dupont pins on the input terminals, I was able to recycle an old 3-pin header from some old electronics bits. I soldered that to the 5v and GND from the molex, then jumpered the GND to IN.
At the other end are your three typical NO - COM - NC terminals. You connect your AC active wires to the COM and NO terminals. When the relay activates it will close the NO (normally open) and open the NC (normally closed), shunting your power through.
I've added a few shots of how I did mine. The 5v for switching is from a PC connected via Molex, should work the same from USB unless your Pi provides standby power.
I took the shots of the relay wiring a year ago, been working well since, all hidden away behind a panel. I apologise for photobombing your thread
I just added a shot of the panel/switch at front, for context only, you don't need it. It is the original mains power switch for the cab, so I left it in. It is actually unnecessary now because I added a PC-style power plug port at the back which includes a switch, fuse and LED. Also added a line filter. Anyway, none of it triggers the relay or is otherwise important, it is only for context.
Hopefully it all passes the Scott test
EDIT: Mostly I power up/down the cab with a discreet momentary switch at back/top/left of the cab (reach up/behind with left hand). This powers up the PC, which then powers up everything else via the relay. Very noob-friendly. The fused mains power switches I mentioned mostly just stay on, though I sometimes turn off the one at the back if not using for a long time.