If you own the home then you can get a mortgage. Credit Unions usually have better rates because they are non-profit and do not pay tax or shareholders like banks and so can charge less. Talk with several lenders before you decide on what option is best for you.
This time in your life it is easiest to start proper estate planning and you are too young for a reverse mortgage. See an estate planning lawyer for help to get an idea of what opportunities you have now to protect the equity you have built up.
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Shop around. A regular mortgage is expensive as you pay for loan origination fees, inspections and appraisals and all the other closing costs associated with the loan. The trade off is a lower interest rate than other types of loans. A line of credit is not my first pick either. A home equity loan can be easier to get. Some banks offer NO COST home equity loans as a marketing tool. You pay nothing, although it can be a slightly higher interest rate. Interest rates are so low, that I think a slightly higher rate for a no cost loan might be a good trade off. Again, shop around and do the math. The math being...how much more interest would you pay or save versus the costs you would be paying or saving, and over how much time until you pay the loan off or sell the house.