Actually if I were you I'd consider two companions.
No matter what animal you decide on for your horse, it will most likely be a herd animal.
If you decide to take your horse away (trail ride, show, hunting,) the companion animal would be alone and likely to be distraught.
I agree that three is the minimum number. With TWO, they tend to get very attached to each other, and get upset, distracted and often downright unrideable when separated. With THREE (or MORE), there isn't quite the bonding.
I like our small standard donkey. He lives on air, gets his hooves trimmed every other time the farrier's out (they grow slooowwwwly), he gets the same spring shots and a dewormer lasts him through two dewormings, he's that small. He doesn't get freaked out if we leave with the others, he's too smart for that.
I've done the donkey route. Tried to close the donkey in the barn while I rode, but it sounded like an elephant (a very angry elephant!) was locked in there. She was so attached, she couldn't handle it. She ripped the door off the hinges and came after us once!! We ended up just riding all around the property and she would mosey along with us.
Had 2 large goats. They mostly hung together, not with the horse.
Had a pygmy goat and horse almost killed her. Too small.
Goats are really the most cost-effective option. Get 2 large whethers and you're set. If they're big enough, your horse fence will keep them in. I always had trouble keeping the little guys in fence.
I really wouldn't suggest a second equine, they will get so attached to each other, you'll never be able to enjoy one without the other.
My llama has never tried to eat my mare's tail. She is a Haflinger and if anyone or anything messed with her beautiful blonde mane and tail .... Well, let's just say I would not be a happy camper! I actually heard that goats were apt to chew tails. Llamas have no upper front teeth so I am not even sure they could do that much damage if they wanted to.
Oh, crap, I forgot about the tail-eating. The goats ate my horse's tail thru the gate - he just stood there and let them have at it!!
This is going back a good many years (back in the teen years before I had a farm-full), but I was mortified to show horse with roached tail! I still laugh at those photos of that summer's shows. At least it made his HQ look bigger!
My horses have lived alone. When one goes to the training barn, the other is left home alone. They can "see" horses down the street when turned out. They handle it ok. We play music & leave the lights on longer. I know it's not perhaps ideal, but it works for us.
When I was in your shoes -- and I really didn't want the headache of another horse -- I got a miniature donkey. Excellent choice. He's an easy keeper, cute, entertaining, adorable, etc. He does require the same care as a small horse (hooves, worming, yearly shots); but he has caused no trouble whatsoever, and my horse is very happy to have him here!
ETA: The horse does not mind leaving the donkey, but the donkey cries when the horse leaves him. I leave the donkey in the round pen with a flake of hay when I have to take the horse away. For every day riding here at home, I just leave the donkey loose. Sometimes he follows us. He's very clever.