If you only have enough money for one major piece of furniture, obviously you should get something to sleep on. You don't have to have a proper bed, but a mattress that is at least full size is a wonderful thing to have.
When you don't have much money for bed linens, plain white can look lovely.
If you need to dress up your bed a little more, adding one bolster and a throw adds a great look to plain white sheets and a white duvet.
Here's an example of pillows sewn from old jeans and a headboard made from repurposed used boards.
The same kind of mix can apply to your living room. You will likely have some hand-me-down pieces from your family, and you can make them all work together with the proper space planning.
Don't have a matching set of chairs? No sweat. A mix can be really fun. If you have a bunch of different wooden chairs, try painting them all the same color.
Try different arrangements until you get a good flow. Don't hesitate to re-arrange and experiment on a regular basis.
If you are in a tight space, find multifunctional furniture. This cabinet transforms into a home office.
You probably won't want to change too much in a rental, but a great skill to learn is some basic electrical skills. Store that ugly dusty brass light that came with the place and make your own pendant lamps from a simple light kit and a cheap lampshade.
One bold move can make the room, like the strong black and white rug in this room. Stores like IKEA, Pier 1, CB2 and West Elm have great rugs that are reasonable priced, especially during the sales where they sell all of their floor samples.
A sturdy tray table can become a beautiful bar with a few spirits, flowers, and some lights!