custom shower

What is the best base for longevity (no leaks in tiled shower; kerdi; hot mop; or mortar and liner?

Any of them, if done right. If you take into account other factors, my preference is for a surface applied membrane, Kerdi is one that I've used. My personal feeling is that it is best to put true waterproofing as close to the tiled surface as you can. In this manner, there's very little that can either get wet, or if it does, it dries out faster. Both the hot mp and traditional mortar bed with liner have a thick layer that can get damp. Now, if they're done right, it shouldn't accumulate, but, putting that waterproofing embedded in there with lots of additional layers and work on top of it makes it potentially prone to damage during the subsequent steps. With something like Kerdi, you can actually finish the walls most of the way to the floor before you even install the shower pan.

I checked out the Nobel website and liked what I saw, especially the linear drain. My shower will be 3' wide by 5' with a drop in tub at the end (L-shaped not linear). Are there issues with linear drains?

A linear drain is bigger, thus, if you aren't careful when installing, there's more places it could leak. But, if you are careful and follow the instructions carefully, they should be as reliable as a conventional drain. And, they open up other choices for floor tile (i.e., the possibility of larger tile that wouldn't fit on a concave base). Keep in mind that smaller tile, generally, are a safer option, regardless, since there are more grout joints - this gives you more potential grip while standing there. SOme tile are VERY slippery, and you should choose carefully for any that you want in a wet floor area.