Hoping to improve my health

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Hello! I'm Larkin. I'm hoping to improve my health and lifestyle. I'm hoping to eat more moderately and exercise more often. Today was a failure on both counts, I'm afraid, but I'll try again tomorrow.

I'm 5'1" and 114.6lbs. My body fat percentage is very high. I was once stronger than I am now, but I was very ill and was down to 66lbs, and put all of the weight back on as fat.

Currently, I run 1.5-2km every day. I do sit-ups and the odd bit of yoga, though my house doesn't have floor space big enough to do many exercises. I don't aim for any specific calories, usually, but count them for diagnostics; I can be anywhere from 500 to 1500. Should I aim for 1200 rather than letting my intake fluctuate so much?

What should I do about strength training? I'd like to start it, but I can't afford to go to the gym.