When you decide on the type of swimming pool you want to install in your backyard, you'll also have to choose the way it will be lined. Fiberglass pools are prefabricated with a gel coating and don't require any extra type of liner. Vinyl-lined pools are customizable, but you have to replace the liner every couple of years as it wears out. Meanwhile, concrete pools are also highly customizable, and they're usually lined with tiles or coated in plaster.
It's hard to say which type of in-ground pool liner is the best since different considerations come into play. The advantages to vinyl-lined pools are that the initial cost is lowest with them, and they can take a variety of shapes since the liner can be stretched to fit. Plus, the vinyl is nonporous (therefore stain- and algae-resistant) and is smooth to touch. However, vinyl liners have to be replaced every decade or so, and the cost of a new liner is typically a few thousand dollars. In addition, the vinyl is vulnerable to gashes, so if you have a pool that will see a lot of roughhousing, you could end up having to replace the liner relatively often.
Concrete pools are more expensive to install than vinyl-lined pools, but they can literally be any shape or size you want. The downside is that they have to be refinished and re-tiled every decade or so, and that can cost around $15,000. And since they're porous, they require more chemicals and cleaning than other kinds of pools.
Meanwhile, fiberglass in-ground pools are kind of like massive bathtubs. They're installed as-is and offer the advantage of relatively low maintenance costs since there are no liners to replace and fewer chemicals required to keep them clean. However, size and shape are very limited, and the up-front costs are the highest of the three types of pool.