Fixing a toilet deceptively complicated, where did I go wrong?
One problem (and not just with home cheapo) is that there are many models of toilet that all do the same thing, with somewhat different and not always compatible parts. Some have 2" flush valves, some have 3" flush valves - etc. Two problems with home cheapo and lowes and other things like them is that the help are often not particularly knowledgeable, and the selection is not comprehensive. Quality on many parts is "hope you live close to the store, because you may need to take it back for a replacement" but that is hardly limited to them, as many of the same poorly made parts are available elsewhere. A real plumbing supply will have a wider range of parts and possibly better quality as well, but they will come at a higher price, and some won't sell to the general public (being setup as wholesale only, they don't want to collect sales tax or compete with their regular, high-volume customers, who are plumbers. If they do sell to the public you will pay a lot more than your plumber does for the same item.)

In your case you probably would have been money ahead to simply buy a whole new toilet (all parts compatible), rather than call in the plumber. The cheapo near me has 18 in stock that cost less than $200 for the complete toilet. I'd personally avoid the cheapest of those, and I'd factor country of origin into my buying decision. It's not a thing I buy often, and having it break is annoying.

Brass is not inherently better than plastic. Either can be made well or poorly, and for some water supplies, plastic is a far better idea. No fill valve lasts "forever."