I am interpreting this question as a " Should I pay cash vs take out a mortgage? " question as opposed to the more basic "Should I buy vs should I rent" As far as a mortgage is concerned, you will qualify for a housing expense equivalent to about 33% of your gross income. Using a $ 50,000 pension, that will get you a mortgage payment of about $ 1,400 per month including property taxes and home insurance. Using a 30 year mortgage of 3.875% your monthly principle and interest cost is $4.70 per thousand borrowed. By the way, lenders will not even think twice about lending you the money on a 30 year term provided you qualify.
You might want to consult a financial planner. But your decision wether or not to take a mortgage vs paying cash should be based on what your monthly income vs expenses allows you to do. Can you still live comfortably if you had to pay the mortgage each month? Will you still be able to do everything you want to do. If the answer is no, then pay cash.