Do people use them because you have to have a number in that spot? Or is it just custom?
I prefer to buy tack that I can use in more than one occasion so my choice is the fitted pad. If I have to wear a number I'll clip it to the bridle like dressage riders do.
They came into style awhile ago as just one of those "new" fad things and were conceived from the square dressage pads, but have stuck around. As far as I know, numbers aren't REQUIRED to be on the sides. Some judges like it, some don't. I've never heard of any specific rules either way, but it's always a good idea to ask when you register for your classes.
From experience having the numbers on the side of the pad work wonders on saving your clothes!! Putting the numbers on your back with safety pins, or even number pins breaks the threads of the material and can cause holes. Especially, if there's even the slightest breeze. Another thing I don't like about number on backs is they tend to make your back look like it's bending in a way that it's really not. Having side numbers eliminates that. Another bonus is if you have multiple wardrobe/tack changes, you just slide that sucker in there and away you go.
As for the bridle numbers, I've never really seen them outside of the dressage/eventing arena, and probably would be discouraged by 4-H.
For the OP, a fitted pad for 4-H works great and is more cost effective, as they tend to cost less than the "square" pads. But the backs may have a tendency to slide to one side or the other, so you just need to keep an eye on that.
As for attire, being in 4-H, the judges really aren't supposed to judge you on the quality and fit of your clothes. As long as you have the basics (or any attempt at) you should be good. Basics from head to toe are black field or dress boots (and YES the el cheapo ones are perfectly exceptible for 4-H), breeches (like others said grey or tan is best), if $$ is a big issue, I have seen kids wear cotton leggings in the appropriate colors. A collored shirt (sometimes you can find an old tuxedo shirt at a thrift store and that will work just fine), some type of pin at your neck (look in catalogs for ideas, then hit the thrift stores!), and yes ideally a proper hunt coat is what you want, but if it's way out of your budget, then any sport coat that fits you and reaches the bottom of yuor butt cheeks will work. If it's to baggy you can use LOTS of safety pins (or sew) to bring in the sides. And a hard hat is a MUST. Black is ideal, but you can use a black cover if you have a colored helmet. I have seen kids with hot pink ones win in 4-H shows. Gloves are not a requirement but they do tie the whole thing together.
Look at magazines and catalogs for what the "ideal" look is, and then do your best to re-create it. It doesn't have to be perfect at this point. 4-H is about learning how to care for horses and horsemanship, not what clothes you wear. They want you to get as close as you can afford, as long as you are showing that you understand what is ideal and are doing the best you can to achieve that, they are happy.