A free standing wood stove is probably the most energy independent option. It will run with no power, although some do have blowers, and in many houses folks use an assortment of fans to help move the heat around better. (depends on the exact setup for details) - however the worst case is simply that everyone has to camp in the room with the stove till the power comes back on. Most likely the rest of the house would get chilly, but the stove will keep the pipes from freezing.
An insert is probably not an option for you, since it needs a fireplace to be installed in, and you said you don't have one. - however it is like a stove in that it will burn w/o power, but is a bit more dependent on an electric blower for heat distribution.
A pre-fab "zero clearance" fireplace will be a net heat looser, unless you get an EPA approved heater/fireplace unit, in which case you have about the same situation as an insert - burns but doesn't do as well at heat distribution.
All of these options require cord wood, which can be purchased cut & split at moderate expense, or purchased in log length / scrounged where you process it your self - this is the absolute cheapest way to heat, but you pay for it in "sweat equity" Cordwood is also mostly a local source fuel, and the price tends to be fairly stable and only indirectly effected by global politics / price of oil / distant events.
Pellet stoves require electricity to operate, but not huge amounts, they can be run for considerable periods of time on battery backups of various sorts, or a small generator, although this takes some pre-planning. Pellet fuel can be expensive, much depends on when / where you get it, and there have been shortages in the past. Pellet stoves are also more complex, and like any item with lots of moving parts, can be subject to breakdowns. Some folks find them annoyingly noisy (depends on model, where it is, and your tolerance levels) Pellets are probably the most convenient, neatest, and lowest effort of the wood fuel alternatives, but you pay more for that convenience.
LP and Natural Gas (essentially the same units except for some minor parts changes) may or may not be able to function w/o electricity, depends on the unit, and obviously are petroleum dependent.
If you care about appearance, cordwood will give the original "natural flame" that everybody else tries to imitate. Some of the gas units look fairly realistic, but all are still imitating the "real thing"
For costs - I haven't priced gas units, but my understanding is that they are fairly reasonable, and their venting requirements are also pretty low cost and easy to meet.
Cord Wood, the stoves can be less expensive, but there is a wide range of costs depending on how fancy you want to get. However wood units will require the most expensive chimneys, with the most limitations on how they can be vented.
Pellet stoves are more expensive than wood stoves, but have easier, less expensive requirements for venting.
Except for the actual gas plumbing, some or all of the installation work for any of these could be done by a good DIY person to save on that part of the costs.
As you can see, there are a bunch of tradeoffs involved, and you need to make your own calls on how to decide which way you want to go on them.
Gooserider
