Breeches are important for a number of reasons. They are way more stretchy than jeans and so will be more comfortable to ride in. As well as being way more comfy than denim, they allow your instructor and judges to better see your lower half and so allowing them to judge and instruct you more effectively. The suede patch on the knees also prevents rubbing from the saddle onto your knee. I wear breeches every time I ride and I would honestly not consider wearing anything else - I used to ride Western in jeans and it was fine for that but for dressage no way! I wouldn't worry about being self concious in your breeches - I used to be but if you ride at an English barn it's quite common for people to be wearing them. I think you'd get stared at more if you weren't wearing them! They're skin tight but they're not SO skin tight that it looks gross. Kind of like a leggings type of thing, anyone can wear them.
You can buy them at any equestrian store, they'll usually sell apparel as well. I don't know where you live but if you're in Canada or the USA you can find some good ones at Greenhawk. They go anywhere from $25 - $250 depending on what you want. The higher end of the spectrum is really for very serious competitors, so a pair of cheapier breeches will be great! They're very durable - my first pair of breeches got a hole in it after 2 years of serious wear and tear.