If you're on a budget I would highly recommend searching/combing through ebay
and there are tack swap groups on Facebook where I've personally found lots of good conditioned show coats, breeches, and tack.
Helmet, I recommend Troxel as a first schooling helmet, and then if you get more serious I currently ride in a Charles Owens and love it.
Gloves really are a must in my book, I guess it would kind of depend what kind of horse you would be riding. I ride a headstrong stallion so I would never ride without gloves or my hand would literally be torn up.
Paddock boots w/ half chaps.
You might not need them but its always nice to have your own crop and spurs.