There isn't really a hard and fast rule, but in general here is some advice for your different equipment.
Lights: You should start turning them on at some point during the cycle. Doesn't really matter when. After you get your rockwork set up, it's a good time to use a PAR meter and map out the PAR in your tank. You may still be able to rent one, or you can turn your phone into one with an underwater enclosure and the Photone app. Or you could buy one, but they're quite expensive compared to their utility. You really only need to measure PAR once every few years.
Heaters: Put as many layers of control on them as you can find. On my tank, my two heaters are plugged in to an Inkbird controller, which is itself plugged into my Apex. Heaters are the most common failure point in aquarium so you want as much fallback and redundancy on them as possible.
Refugium: You can start this immediately, but probably best to let your cycle finish before you start trying to grow chaeto (or whatever else you plan to grow). It'll compete for the same nutrients your nitrifying bacteria use, so you want to let them get established first. And really, you don't exactly need this from the start. Might be best to wait until you have fish in the tank to start producing waste products.
Skimmer: See refugium, though for different reasons. The skimmer does three things: It oxygenates your water; it skims out waste products before they decay into nitrates and phosphates; it skims off some (but not all) toxic byproducts, such as coral toxins. As with the refugium, turning this on too soon will starve nitrifying bacteria, so you want to let them get established and make sure there's something in the water for your skimmer to skim before you turn it on. After your first couple of fish is a good rule of thumb, but you can have it on earlier. Just be aware that if there isn't enough "stuff" in your water, it may overflow.
Rollermat: See above. Rollermats remove solid particles down to a certain size from your water, again preventing them from decaying into things like nitrates and phosphates. And pretty much the same advice. You can turn it on whenever, but it'll slow down the growth of nitrifying bacteria and doesn't really help until you have enough waste to need to filter it out.
MP60: Just make sure you don't have them directly opposite each other. For a peninsula, I'd put one on a side pane, probably about midway down the tank, and the other on the glass opposite the return chamber. Position one high enough that it'll create some surface agitation, the other deep enough to have strong turbulent flow through the mid levels of the tank but slower flow along the sand bed. Too low and the MP60 will kick off a sandstorm. You can get fancy with these to create things like standing waves, but personally I think it's best to just keep flow random.
One thing you didn't mention was a UV filter. I'd recommend reading up on them and deciding if you want one now, before you've got everything set up. They're kind of a pain to plumb in after the fact.