You should get the biggest, longest, possible mortgage that you can afford - period. People who can pay cash for a house can equally leverage that money MUCH better for a rate of return, safety, and liquidity - something that having all equity/cash tied into the house does not provide. You see equity has NO rate of return being tied into the home - it only grows based on appreciation...but it also can depreciate.
Being debt free does not just mean you have no debt, but that you also have the financial resources to pay off any debt. Mortgage debt is the smartest, cheapest, and most leveraged debt for building wealth through home ownership. BUT ONLY IF YOU USE THE EQUITY FOR GROWTH in a safe side fund - and not vacations, flat screen TVs, and other consumable stuff...that will bury you. Example - If you could afford a 15 year mortgage with it's higher payments, you'd be far better off to get a 30 year fixed and take the difference in the payments and invest in a conservative tax-deferred side fund earning in today's about 7.5%. In less than 15 years you would be able to pay off your 30 year mortgage (as if you had the 15 yr) and have a lot more to do even better things - more investing, college tuition, etc...there is SO much folks can do if they managed their finances smarter.
Some of the unfortunate home owners who lost their homes on the Gulf Coast during the hurricanes a couple of years ago now realize if they had their equity seperated, rather than having their house paid off, they could have had the resources to build again, move, do anything to move on with their lives. Lenders with notes on the homes were more relaxing in taking payments during the misfortune. But here's the key point, throughout all of this if the equity was seperated, it would still be earning a rate of return, and available TAX FREE without jumping through hoops to get it. Try getting a home equity loan or 2nd mortgage when you're out of work or disabled - it won't happen easily if at all. The equity management systems and principles we use for our clients is so powerful for building wealth. Most folks only know what they know...including the professionals.
When executed properly, this is a predictable methodology that will leave you in a MUCH better financial situation. You need to factor in you net after tax cost of the loan...for example if your marginal rate is 28%, and you have a 8% mortgage rate, your after tax rate after your interest deduction will be more along the lines of 6.5% depending on your particular tax situation. But the other factor is aqcuisition indebtedness. Currently, you can deduct mortgage interest up to a $1 million mortgage amount. So using an example of having a $300,000 mortgage on a home you paid $200K cash, that is now worth $500K, and let's say you paid down your mortgage to $180,000...if you decide to refi for 80% of 500,000 to pull cash out, the deductibility of that interest is limited to $100K over and beyond the original acquisition indebtedness - which is the amount of debt still outstanding at the time of the refi..in this case, only $100K above $180,000 or $280K, NOT 400K. There is an exception to get around this rule for deducting more than 100K - and that is to use the proceeds for capital improvements. So if you factor in your net cost of a mortgage based on your marginal tax rate, and the opportunity cost of investing the cash you have to safe seperate side fund for safety, liquidity and rate of return, you should not dump cash into your home. Again, as long as you have the funds to pay off the mortgage, take advantage if the deductions, while you let your equity work for you.
We use this Tiger Woods analogy - many times the media, and gurus try to sell us on buying the latest version of Tiger Wood's club...what we teach folks is how to learn his swing! That is where the real genius and power comes from to accumulate wealth and become debt free.
If you have specific questions on how we can help direct you on this process, feel free to email me direct at firstname.lastname@example.org
I hope I've cleared up some of your questions.
Calculating the tax savings is really a task for an accountant as it depends on your overall financial situation. Since you have a standard deduction anyway, you'd have take into account that itemizing your tax deductions may not necessarily be as advantageous as you would expect, especially with a purchase price of only $100,000. If you end up financing, you'd want to put at least 20% down to avoid private mortgage insurance.
I hope this helps. Good luck with the purchase of your first home.