Which business model should i use?

I am starting out as a graphic designer, I have a contracted position at a local printing company. I've learned that if I register myself as a company, I can avoid paying taxes on that income by using it to purchase supplies and other related expenses; however I know next to nothing about finance and don't know if it would best to organize myself as an LLC, corporation, partnership, or other entity. I also am unsure as to what expenses I can "write off" or how a business actually files its taxes.