Cheap Amazon stuff has come a long way over the last few years, so much so that I find the upcharge for brand names to be harder to justify than ever. Here's my 'budget' recommendations:
Lights:
Nicrew, Smatfarm, and Viparspectra (all on Amazon) and Noopsyche (their own website) are all great lighting options. Been running some of these for a few years now without a single issue. Agree you would want two fixtures to get good coverage and avoid shadows, but they don't need to be particularly powerful for a 40b.
Pumps (both internal and external):
DC is definitely the way to go. Never had a problem with jebao or hygger stuff. I particularly like Jebao's newer 'EP' line of pumps. Silent, powerful, efficient, and very adjustable (1% increments from 30-100). Jebao even has a Vortech clone now if you really want that no-wire look for your wavemaker(s). The exact type and size of pumps you'll need will depend on your setup though and what kind of corals you'll be keeping.
ATO:
I like any of the cheap optical ones since they are simple, compact, and reliable (and yes, cheap

). I own 5 from a few different sources and have never had a problem. I recently got one of these for just $30 and so far it's been great:
https://a.co/d/02QcZBF
Sump:
I always make mine out of Aqueon tanks so I can't comment on off the shelf acrylic sumps. For a DIY sump for a 40b I'd probably use a 20g long.
Dosing:
Kamoer X4 Pro can be had on AliExpress for just over $200. Great value for a highly accurate and reliable doser. This is one area where I would skip the Jebao because their dosing heads are driven by friction between the motor shaft and the plastic wheels of the peristaltic pump. They wear out over time, especially in a salty environment, and the shaft can slip, leading to inaccurate doses.
For $120, this one also looks very promising, but will need to see more reviews. May end up being an unbranded red sea doser?
https://a.co/d/bjedbo9
Cycling:
Live sand works (according to Aquabiomics DNA testing)! Use it!
FritzZyme 9 (or turbostart 900 if it's refrigerated) and BioSpira have been tested to be the fastest cycling bottle bacterias.
Rock:
Tampa Bay Saltwater is an excellent source for true live rock, but if that's too pricey dry rock is fine too. The 'Money Saver Aquarium Dry Live Rock' from saltwateraquarium.com is a great value.
I'm not up to date on skimmers in that size range unfortunately so I don't have any specific recommendations there.