I don't know exactly what you're asking for but here's a few things that may be helpful.
First, I will address the notion that renting is somehow better than owning and vice versa. When you rent a home, make no mistakes... you ARE paying property taxes and you are paying for the maintenance and upkeep on the home. The only difference between owning and renting in that respect is that you aren't required to come up with $2,500.00 on short notice when the AC or furnace fails. However, you are paying for those repairs whether they occur or not, as a part of your monthly rents. This is a simple question of economics... a real estate investor is no different than a woofer manufacturer. They have to include ALL costs into the rental price (including property taxes) and they have to add a certain amount of buffer over and above hard costs and profit, in order to pay for big ticket repair items. If they don't do that, they won't be profitable and will eventually go out of business.
The idea that owning is better or vice versa is purely a subjective one and it is different for each person in each situation. If you're not mechanically inclined or you don't have time to do maintenance on a home, you might be better off renting. Or, maybe your job requires that you move from place to place every year or so. In those cases, renting makes the most sense. However, if you have a job that will likely never require travel and you have either the knowledge and/or financial resources to pay foe maintenance as it's needed, then buying is probably better. In the end, there is no right or wrong in economics... there is only subjective best choices based on circumstance.
Also, the notion that everyone should own a home is preposterous. Everyone who wants to own a home should strive for home ownership but those who don't own their homes are no better or worse than people who do, if that's what works best for them. Do what works best for you and ignore the advice of bigots.
As for paying off a home as opposed to having it mortgaged... having a home paid for opens you up to potential losses that a mortgage can protect you from. For instance, if someone gets killed on your property or if you are sued for any reason and are found to be liable, a owned home becomes accessible by those creditors. Doesn't matter if it's all your fault or none your fault either... all that matters is that a judgement has been issued against your assets. But, mortgaged real property is not accessible by creditors due to the fact that there are others who already have a legitimate claim to said property.
There is also the cash layout to be considered. A 15 year mortgage will consume more of your ready cash each month than a 30 year mortgage, so from an economic standpoint, the shorter term loan costs more to service and leaves you with less cash with which to make other investments that could potentially net you a profit over and above the amount you're saving by not taking out a 30 year note.
By opting for a thirty year note you can look at the money paid in interest as a loan that allows you to have more cash on hand in the here and now. And of course, when you borrow money, you pay the lender a profit.
Personally, I will probably always opt for a thirty year note, as it allows for a lot more freedom in the here and now and you can't look 25 years down the road at what you might be able to do with that saved money.... aside from actually saving it.
Another very important thing to consider is the purchase price of the home. Buying a home at market price is not a good way to start an investment. Especially if you don't have a lot of money to put down, as when you do so you put your entire investment at the mercy of the stock market. Homes do not and, frankly, should not always rise in value and as we saw in 2008, when you have little or no equity in a mortgaged asset, you are locked into paying for something that costs more than it's worth. Thus, if you find yourself needing to sell it, you are in a lot of trouble. This is evidenced, again, by the various housing market crashes we have seen in the last century. The most recent being in 2008.
If you want to buy a home, shop the market well and loosen your criteria as much as possible. There are a lot of homes on the market and each and every seller has a different reason for selling. There are plenty of motivated sellers out there who have a home they need to sell and who can afford to take a loss on the sale simply to get rid of a headache. So... don't be afraid to make an offer that's well below market value. You aren't insulting the seller by doing so, you're simply telling them what you need and asking them if your needs and theirs can be met at that price.