Diablo 1 HD Hellfire Mod | Awake

I would like to procure a full set of the Brilliant recipes at some point, as I want to build my gear around maximum damage reduction, and try to get +all stats and %damage to mana on the randoms.

I'd be hoping to get this by the end of Nightmare, or at the very least before Torment.

Recipes are just rare items that have a chance to appear like any other magical item. Your best bet is to farm anywhere you'd usually do so: the three chests in Lost Treasure or the Lair of Lazarus are probably your best, quickest chance.

Might I ask, though, why are you restricting yourself to Nightmare difficulty? Recipes are quite rare and there's a good chance you'll be severely overleveled for the beginning of Torment, it seems a meaningless restriction.

What level are you supposed to be for each difficulty level? I'm 28 and still in Normal, trying to get to 32 for Blood Ritual before I fight Diablo.

Just whatever you're comfortable with. Only in Tchernobog there is a minimum level required for entering any dungeons within any difficulty.

On a personal note, I was 30-ish when I successfully completed Normal on my first character in Belzebub

In any case, I would like to get the Brilliant recipe set as early as possible to combat the resistance penalties of Hell and Torment.

Speaking of which, how rare is it to find an item that has both +all stats and +resist all on it?

Good (or at least decent) rares are pretty common. Once you'll be able to access Lost Treasure cave on 2nd difficulty, you're gonna have plenty of rares, uniques and set items as well as low level recipes.
Not quite sure about Brilliant recipes though, I think they are quite high level and if I recall correctly I've found these only on 3rd difficulty and beyond.

The documentation lists the suggested level advancements at 27/35/42/+ but those are, of course, just suggestions. Playing hardcore characters I usually manage to punch through Normal about level 30-32, but obviously I'm paranoid.

The Brilliant recipes seem to be around levels 25-37 (an annoyingly large number of them don't have their levels in the documentation), which would make it possible to collect the set around the end of Nightmare but it would be a lot of grinding.
I don't mean to tell you how to play the game, all our characters have hobbies, I'm just concerned you're going to be let down. If you're still playing that Necromancer they can definitely take a punch but they usually want to avoid getting hit instead, what with the horde of minions and all.

I'm 28 now and my minions are actually starting to become formidable. They can survive against non-elemental Hell mobs now, such as Knights and Snakes. They still get destroyed pretty easily by anything with ranged attacks, but I'm able to deal with those fairly easily.

I'm not disappointed with Necro at all, it's just a late bloomer. Takes the class a while to come into its own, but once it does...

Anyway, I think what I'm going to do is try to punch through Normal mode now, then I can do some loot grinding in King Leorics Tomb and Chamber of Bone in Nightmare, where there's lots of chests. I have the spells I need at this point to carve through those areas fairly quickly.

Finding recipes is a bit like finding runes in Diablo 2. Your best bet might be the Cathedral levels in Torment because there are a lot of monsters and I believe they can drop most, if not all, high level recipes.