How do I make my back yard nicer?

So I ve rented a place, I m thinking 1-2 years max, but the back yard is an absolute disaster. We have knotweed in the garden and weeds all over the grass, and I m not even sure if it s "lawn" grass or not lawn grass. Someone already tried to suppress the knotweed about three years ago, but it s pushed through the landscaping fabric so now there s just landscaping fabric under the garden, under the grass, and under the poorly-laid patio stones and it pokes out in places, especially in the patio stones.

Today my roommate and I tried to dig up the mass amount of weeds in the garden and we put down some river stones to try to help suppress the knotweed and make it look nice at the same time, and we ve potted some flowers, but holy hell those stones are expensive! She spent $30 on what we have and it s barely enough to cover half of the garden, and it s not even a thick enough layer to keep the knotweed somewhat at bay. Do you have any suggestions for us? We have grass seed, and I have all the time in the world, but I don t have any money and she s leaving for her honeymoon in 4 days.