If you're playing on the last stable release:
Hideous is equivalent to ultra-violence, Grotesque is equivalent to Hurt Me Plenty, and Ugly is equivalent to Hey Not Too Rough. Much like classic Doom, these only differ in the amount of monsters, so you're not "missing out" on any mechanical depth or anything. I'd say that Grotesque is the "intended" difficulty, since HD's monsters are more dangerous than normal. Homely removes bleeding and reduces damage for a gentler intro to the combat mechanics, while Grimdark adds extra damage and fast monsters so it's the "hardcore" mode (Spooky is "Grimdark with less monsters"). Don't even bother with Nightmare, it's basically unplayable IMO.
If you're playing on the unstable / development master:
The difficulty levels are now completely equivalent to classic Doom's default options, and HD-specific difficulty mechanics are in the HD Options menu with Casual, Normal, and Hardcore presets available. Here I'd say Grotesque + Normal is the intended difficulty (Hideous + Hardcore = Grimdark, Ugly+Hardcore = spooky, Homely + Casual = the old Homely).
Really though, all these options are there for you to adjust as desired. There's no "right" way to play HD; it's meant to be a bit of a sandbox you can approach in your own style, so don't feel obligated to play a certain way if you find it too easy or too hard! Do what's enjoyable for you.