Don't forget to consider boarding houses or roomettes or bachelorettes; I stayed in these in college and loved them. They come furnished already; you just pay one price and move in. Some even supply small appliances; they are a great way to start out becuz the cost is much lower than a place of your own.
Sharing an apartment with a stranger can work out or may turn out badly, so that's why I opted for the others. I have done it all; roomed, bachelorette, apartments, house, and even been a landlord and ran a rooming house for women.
Many rooming houses have for women only or men only, which is the best way. When they get mixed, problems can occur. A well-run rooming house can turn out to be a gem; some even offer lunches or dinners for an extra cost; or you can just rent the room. This is especially great for single people and a good way to save up money for an apartment or home of your own down the road.
Most rooms are big enough to have a bed, night table, dresser, small table and chair, a tv, desk, and closet. Some even a have a kitchenette or den that you may share with other people. Look around and ask around at places like churches or colleges/universities that often know of the best places. Some bachelorettes offer a bedroom and livingroom with a small kitchenette; some have private baths; some shared. It depends on the place; and the price usually reflects all the extras you include like phone and internet.
I recommend that you put some money in savings every pay check; and leave it there. Put it in a non-checking savings so you can't get it out without making a trip to the bank. Take your time and look around to find the best place. Unlike apartments, you won't have to pay deposits and other fees: just one month in advance and that's it. Some charge by the week or month, as you prefer (and I just loved that option).
Today, with things so expensive ~ rooms, roomettes, and bachelorettes are a real bargain. They are less hassle, less expensive, have less baggage, no leases, and so on. You only need your clothes, personal stuff, and maybe a bit of linen (like towels or bedding) to start out ... very worth considering.
Wish you the best in your search

ROSEBUD