Cool Tools, Flexible LED Strip Lights, has some nice pictures of LED strip lights installed as counter lights in a kitchen.
One problem with the LED strips is that you might want a housing so they aren’t installed bare but protected inside a fixture. That might make mounting easier and result in a less ‘industrial’ look. Here’s the Amazon link to one:
Superbright LED’s as linked by Cool Tools has a selection of these housings in both aluminum and MDF with lenses, end caps and other accessories. The problem is that they seem rather expensive. The Amazon item is nearly $10/foot and doesn’t include the LED’s.
An aluminum U channel extrusion can be found at the hardware store for less than $2 a foot. It might be possible to use one of those to make your own LED strip lighting housing. There appears to be a lot of this for 3/8″ thick glass edges and that is about the right width to handle one LED strip. The prices are all over the map. National Mfg. N342295 U Channel is a half inch wide, .08 high and 4 feet long for $6.19. Check your local hardware or big box home improvement store with a chunk of your light strip and see what might work. These stores will often have a selection of plastic sheets and things you could use for a diffuser.