Looking back, the two large kilim rugs I bought 15 years ago have stayed with us through changes of taste, a new family, and multiple homes, they were a fabulous investment.
In a rental a rug will also go some way to hiding ugly carpet or tiles that wouldn't be your choice.
Light fittings in rentals often tend to the cheap and nasty. Lamps are a cost effective way of improving the lighting and adding your taste to the space. We had a hideous pendant in our previous rental and the best thing I ever did was replace it. I never regretted the expense of an electrician to take it down, and put it back up before we left.
Buy some simple glass vases (look out for great bargains at $2 shops) and fill with fresh flowers, your space will feel more like home immediately.
Simple peonies, PB Kilim, Titan lamp from Freedom, Wool kilim from Loom, Beaded Chandelier