Landscape edging gives a finished edge to planting beds. It also can keep mulch, either organic, like bark mulch, or inorganic, such as rocks, inside the beds. Additionally, it can keep planting beds from being invaded by unwanted plants that spread by stolons, which can run either on top of the surface or underground. These plants can be weeds or they also may be turfgrass from the lawn itself. Deciding what type of landscape edging to use depends upon several factors. Among these are how much money you have available, how much time and energy you're willing or able to put into the project, how effective the particular edging is at achieving the goals listed above, and what you want the end result to look like.
Dug edging is the least expensive, if you have the time and energy to put into it, because all you have to do is dig. You can either dig a trench around the landscape bed, or you can sink the landscape bed into the ground a few inches. The problem with this approach is that your edging will lose definition over time and will need to be redone periodically.
Plastic is one of the least expensive installed edgings. It's also relatively easy to install yourself, and if it's a type that's dug into the ground, it stops underground stolons from spreading into your beds. It tends not to last very long, though, and some people don't like the look of it.
Metal landscape edging does a good job of keeping mulch in and keeping unwanted plants out, and it tends to be relatively inexpensive. However, it is often more utilitarian-looking rather than decorative. Also, care has to be taken not to buy metal edging with sharp edges, which may cause injuries, particularly to pets and children.
Wood landscape edging, which can be found for a relatively reasonable price, is best suited for larger landscapes. This is due to the large size of the pieces of wood used. Wood edging is laid on top of the ground, so it's good for keeping mulch in, but doesn't do such a good job at preventing underground-spreading unwanted plants from invading. Also, since wood is a biodegradable substance, care has to be taken to protect the wood from decomposing and warping.
Masonry (brick or concrete) and stone edging is even more expensive and looks better than the previous types, but most are designed just to be lain on the ground, which may prevent mulch from wandering out, but doesn't prevent invasion by underground-spreading stolons. When dug into the ground, masonry and brick edging may not go either high enough or low enough for your purposes. And whether it's lain on the ground or dug into it, unwanted plants can grow up between the bricks.
Various professional companies make and install other kinds of edging. So, for whatever purposes you have, or whatever expense of time and money you can afford, there is a landscape edging that will be right for you.