Sounds like you have the movements down pat!
In terms of tack and attire, it depends on how big/competitive the show is, and how competitive you want to be. In my area, it's pretty rural and most open shows are very small and low-key, usually put on as fundraisers by local 4-H and other saddle clubs. Other open shows are downright huge.
You can absolutely compete in halter with a plain leather halter (lead must match -- leather strap with chain the same color as the halter's hardware). Most important is that it be properly fitted and adjusted. A proper show halter is better, but a clean and well-fitted plain leather halter is perfectly permissable, especially at a small local or schooling show. Most games riders I know that do halter classes for kicks (or because their parents want them to have the experience) just use a clean leather halter and lead. At a show of any size at all, you may find everyone using proper western show halters with all the bling. If that's the case and you're really interested in being competitive, it may be worth it for you to purchase one. While I don't advise going with the cheapest of the cheap, you can find an okay western show halter for about the same cost as a good plain leather halter.
For your attire, the same rules apply -- at a little local/schooling shows, a good, clean pair of jeans and a well-fitting blouse or show shirt will be just fine. At a larger, more competitive open show, you may need more of a "showmanship/halter suit" in order to stand out in a good way. I personally use dress pants (the kind that are more fitted through the bum and thighs with a little stretch to them, NOT the really baggy, "masquerading as a skirt" pantsuit bottoms), a "slinky" style show shirt (a turtleneck works if it isn't too hot -- slinkies breathe much better) and a nice patterned vest or blazer, with a cowboy hat, of course. The slinky and vest/blazer combo is going out of style in my area, though, largely replaced by rail-class shirts with big, blingy collars and cuffs. Most of the 4-H kids at smaller local shows go for clean, pressed jeans and button-down cotton western shirts with cowboy hats, boots, and big belt buckles.
This website may give you some tips and insight for what to wear for what class and level and how to coordinate with your horse's color to really pull the picture together and make an impression with the judge. Hobby Horse Clothing Co. - What to Wear?
Look at the whole "Dress for Success" section for plenty of tips. In terms of buying from that site, it's kind of pricey for my blood, but I've found lots of show clothes at the local Salvation Army and Goodwill stores, most barely used.
For western halter and showmanship classes, most folks at the local level leave the tail natural -- just shampoo and condition, detangle if necessary. In the bigger leagues, some folks opt for a fake tail, but for a beginner that's not necessary. For the mane, you have a couple of options, depending on what flatters your horse's neck more. A loose, natural mane is making a comeback in my area, but the more traditional look is to pull the mane short, approx. 4 inches, and band it off in small sections. You can buy tiny rubber bands that coordinate with your horse's mane color at most tack stores. Some folks skip the pulling, and band their horses' manes at the natural length. I've also seen manes pulled short and left unbanded. If you band the mane, the forelock must be banded as well. Try a few options before show time to get an idea of what looks best. English horses use either flat or button braids, but I'm assuming that you're going western.
You'll want to give your horse a trim to clean up his appearance, especially for an up-close class like halter or showmanship. Do the bulk of that about a week in advance of the show if possible -- little mistakes can even out a bit in that time. Clean up his fetlocks, pasterns, and coronets, any long wispies on his lower jaw, and any fuzzies that stick out of his ears when they're folded shut. You can also knock off the long whiskers on his muzzle and around the eyes---some folks leave them, citing their "whisker" function, but that's up to you. I personally clip the muzzle, but leave the eye whiskers. Do the muzzle the morning of the show... they grow right back and can be funky and stubbly... not good. Also, polish his hooves before he enters the ring. I personally like a clear polish (baby oil works on a budget or in a pinch), but black looks nice on some horses, too.
Good luck, and have fun!!