Cool! I have several relay set ups. It took me a while to really get the concept. Sometimes you have to start small and go through a couple of relays.
The easiest way with a power strip is to take the insulation off the chord for 3 inches and cut the WHITE wire. You always want a low side switch if you can, not the hot side. Then take a length of dual wire, 12 ga. Red/black something to tell them apart. Use that with wire nuts to basically extend the WHITE path to ground, over to your relay. That gives you some distance to have your relays in one place with the 12 volt rail, you use to trip the relays.
I have 2 extension cords like that with 3 plug, but use one for each pump, for timer relays, etc.
So, amps vs volts. You have to match your switch requirements. Really for most things I use a 3O Amp auto relay. It switches with 12 volt and that's what my switching system is.
AC vs DC. Yes, you need a relay for that. And you can get relays that are tripped mechanically. A light switch is a muscle powered relay. I have a water powered relay. It's a flow switch for the water cooled light. No flow/no go.
That is one permission. The other is the timer. Both have to be ENABLED for the ballast to start.
The ballast start is a big AC relay about $75. But, it needs a bit of 12 volt current to keep it open. The timer can't switch 12 volt current. It can only switch 12 volts to ground.
When it does that, it trips the auto relay. 30 A max, lots of current. The auto relay trips the AC relay IF the flow is GO. And it keeps the relay open with electo-magnets that draw a bit of current. Not 30A ever, but for 7 dollars cheap relay and available.
BTW, it also turns on an 5000 btu AC on the same power strip. Fun with relays!
