If it is US, you need to take tax implications into account. Profit taken from sale of your home is taxable. One approach would be to take the tax hit, pay down the student loans, rent, and focus any extra that you can on paying off the student loans quickly. The tax is on realized gains when you sell the property. I think that any equity under the original purchase price is taxed at a lower rate (or zero). Consult a tax pro in your area.
Do not blindly assume buying is better than renting. Run the numbers. Rent Vs buy is not a question with a single answer. It depends greatly on the real estate market where you are, and to a lesser extent on your personal situation. Be sure to include maintenance and HOA fees, if any, on the ownership side. Breakeven time on a new roof or a new HVAC unit or an HOA assessment can be years, tipping the scales towards renting. Include the opportunity cost by including the rate of return on the 100k on the renting side (or subtracting it on the ownership side). Be sure to include the tax implications on the ownership side, especially taxes on any profits from the sale.
If the numbers say ownership in your area is better, then try for as small of a mortgage as you can get in a growing area.
Assuming that the numbers add up to buying: buy small and live frugally, focus on increasing discretionary spending, and using it to pay down debt and then build wealth.
If they add up to renting, same thing but rent small.