I dethatched prior to aeration but only because dethatching with a rake is a lot of work and took me several weeks in the evenings. You should rent a machine. If you're not pulling plugs out, you're not decreasing compaction.
I used starter fertilizer. I now wish I had used the Scotts Starter + Weed Control but it is expensive and I opted to go cheaper. My grass is growing like crazy, though, so it's not a huge deal. Probably any starter fert will do. I used the Tru Value store brand which was a couple bucks cheaper.
I use sprinklers. My house has underground sprinklers in front and I have a smart controller that I setup to water 4 times a day for 5 minutes each time. In the back, I used two hoses with a splitter on the faucet. I started with a couple of sprinklers I had laying around but switched hose to an impact sprinkler and really love it. I watered the back twice a day or more often if I was home more. I think this was enough because I have a lot of shade in my backyard.
The idea is to keep the soil moist to aid germination. You want to do the heavy watering until all the seeds have germinated. I have a mix of fescue and Kentucky Bluegrass and they have markedly different germination times - the KBG takes at least 2 weeks and the fescue popped up in about a week.
PVC fittings for the manifold
Rotation - Brass Impact Sprinkler, the previous owner of my house left some of these, I replaced them with an in ground sprinkler system. Used parts from them for both the keg cleaner and the rotating sparge arm.
There is sealing problems with the inductor tank as others have reported, nothing goes through the air lock, I used silicone sealant between the lid base and the tank but that didn't help, my have to put weather stripping on the lid, but I haven't notice any problems with the beer.
Looks like an impact with a bottom input, on a threaded stake for a feed..
https://www.amazon.com/Rain-Bird-25PJDAC-Sprinkler-Adjustable/dp/B00002N8NR?th=1