Your mother is right (sort of) that if you rent you will be throwing your money away; it's (almost) always better to buy - it's an investment!
I understand your want to move out, you're an adult, and it's time to be on your own. It's a big step, but certainly one you can make.
You need to look at your income and your short-term and long-term future. Do you foresee your income going up over the next few years? How long do you plan to remain in the area you are living in now? These are important things to think about. If you want to move to Albania in two years, you're probably better off renting. If you plan to stay where you are for the next several years, buying is a good option.
Do you have any friends who are interested in moving out as well? Perhaps renting an apartment for the next year or two with others is a good option. It will allow you to be on your own, but reduce your living expenses so you can save your money and buy a place later down the road once you are more stable.
Without knowing what area you live in, and what your future plans are, it's hard to say what you should do. Chek out this site:
REALTOR.com - Real Estate Listings & Homes For Sale to see home listings in your area to see what you could afford if you bought. You can also browse rentals this way to see what sort of place you would be renting.
My advice if you buy and want something small is to look at townhouses and maybe condos. Condos sometimes have massive condo fees (my cousin and his wife pay an additional 1/3 of their mortgage in fees a month), but they are low-maintenance. A small single family home might also be nice, if it's in your price range, but the upkeep is more (yard, mostly). Stop by a local real estate office and pick up some real estate books (they are free) to see what else is on the market. Do some research online to see what you need in regards to a down payment, and maybe talk to a lender to see what you qualify for. If you decide to rent, you need to figure out what you can afford, and also account for security deposits and application fees, as well as hope your credit and income will allow you to rent on your own.
It sounds like a lot, and it is, but it's not impossible. You just need to learn more about the process and your options, and decide what is best for you.
Good luck!