Congrats on the new horse belated as that may be! Welcome to the horse hair-care journey.
I use several detanglers/sprays, depending on the time of the year. Pink Stuff is my general daily detangler because it isn’t super heavy and it doesn’t make the body slippery if I get any on her. I spritz the mane/tail along the root of the hair, then rub it in before I start picking shavings out and detangling. I don’t do this every day, especially not in winter, because it would build up (in summer she gets rinsed a lot so not as much of a problem). A bottle of this lasts ages.
I use Knotty Horse for baths. My girl’s hair can get dry so I condition it very well during baths. I’ll use it in place of the Pink Stuff sometimes, but try not to get it on her body because it makes it a bit slick.

Cowboy Magic is my heavy-duty detangler. I pull it out if her hair is VERY tangled. Just put a little along the top of the mane/tail and then work it through. This one is silicone-based (and expensive) so I don’t want to use it too often.
I prefer a wide-toothed comb for combing out hair. It pulls out less (bristled brushes will just pull out hair if it gets tangled). I comb out manes and tails like I do my own hair, starting finger-combing at the ends then bringing the comb through.
I used to also braid my mare’s mane/tail and bagged the tail, but our current barn doesn’t care for that. When braided, I only detangled once every 1-2 weeks when the braids came down for a bath. I spritzed her with the Pink Stuff but otherwise left it alone. Now that she’s unbraided, I just finger-comb out her mane/tail most days to keep it from looking gross. She doesn’t get it too tangled so this works for us.