I have completed monoruns in steel, ground, dragon and psychic and fighting up to ciel. I have mostly bruteforced my way in all other runs of pokemon games, but needed some more in depth tactic for monoruns.
Dragons was a pain in the ... with only having access to noibats until quite late in the game was no fun. Becomes easy when you get evolved dragons. Not recommended.
Steel was quite hard, especially Charlotte, so empoleon became the MVP of that run.
Ground was okay, some struggles here and there, but nothing too painful.
The easiest of my completed runs was psychic, with access to a lot of different types and many of these quite powerful as well.
Fighting stopped at Ciel, as her archeops outsped all of my pokemon and one shotted. This was my first run however with very little tactics, so this should be possible with some more tactics and planning ahead.
For what is an easy start to the monoruns for your part, I think dark, psychic and poision should be fairly ok, access to lots of different pokemons from the start. Ice as you mentioned would be "almost" impossible as you will only have a vanilite for a while.