Since you rent, there is probably not a whole lot you can do with the house without landlord permission. That may or may not happen, and even if so, you may or may not be reimbursed for your efforts.
If the house leaks air all over, the local utilities offer cheap or free audits, and if the home is bad enough, they may do an 80% quick winterizing on the house for free. Sealing air leaks is much more effective than insulation as far as cost and energy savings go. Once the envelope is sealed, the air and humidity doesn't just fall in and out of the living spaces, carrying heat with it.
Please describe the home more. Square footage, basement or not, construction style and materials. More details will render better answers.
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