There are several types of insert determined by what they burn for heat. The main options are natural gas, electricity, wood, pellets, or coal.
A gas insert has a false set of ceramic logs that sit above a natural gas burner. This is considered the cleanest of the three options, but any insert will be extremely clean-burning, especially when compared to how the fireplace burned prior to the insert.
Electricity is popular for ease of installation and for convenience. Electric inserts do not need a chimney; and cost is very low, since it only uses as much energy as one or two light bulbs for the light. A heater does not necessarily come with it, though, and to heat with an electric fireplace insert costs than it does with other types. Also, if you lose power, your fireplace is useless.
Wood-burning fireplace inserts have perhaps the best resource in the sense that it is easily renewable. So much wood is available that proper management of the already-existing will produce a virtually infinite supply. If you are willing to do the work yourself and live in an area with trees, you can probably get a lot of wood from contractors who fell trees and from trees felled by storms.
Pellet fireplace inserts are recyclers. Pellets are formed from wood waste products, paper, cardboard, and other waste materials. At the moment, transport costs to get pellets can be prohibitive, but that problem should fix itself as more pellet plants open. They are probably the most environmentally-friendly fuel source when you consider how easily renewed they are, how they are recycled products, and how clean they burn.
Coal is hard to light. It can be hard to get—in fact, it is only a real option if you live near an Athracite coal mine—and the mining of it harms the environment. It is not easily renewable, but once started, a coal fire will keep burning for weeks or months. Coal burns so hot, though, that you must regularly replace coal grates and liners every few years or so in a coal-burning insert.