I've used haircutting scissors stolen from my mom (lol sorry) and sewing scissors. I use some sort of all purpose scissors right now that are probably a bit dull for the job but they're serviceable.
You have good advice here. I find that to make a pony feel "finished" it always helps a lot to do something with the hair after cutting, usually wetting it and letting it set curled around a neck or a hoof and making sure you run hot water down the neck to make the hair lay flat. I have a lot of so-so cutting jobs that are helped by making the hair look less brand new like that.
I lay the pony down on her side, but I agree doing it standing up is probably better. Get a pony for reference nearby if you can, pull to see how long her hair is, and cut longer than you want.