I've printed this in everything from 0.04 to 0.2 and it turns out well. Of course 0.1 is the sweet spot on our printer, but yours may vary.
It's actually a very simple model and doesn't require supports or rafts. For printing technique my primary suggestion would be to not be in too much of a hurry as the tail turns out better at slower speeds. For our Ultimaker 2 around 30/sec worked best.
Cutting the channel
In the .stl I've included a 0.2mm solid bottom before it moves on to printing the channel. This makes the print look a bit more finished, and I like to ensure great adhesion to the build plate.
You'll need to use a razor blade to remove this from the bottom channel. I recommend placing the dock with the front edge and tail resting on the cutting board and then running the razor down the channel away from your hand and toward the board.
You definitely don't want to hold it in one hand while cutting out the channel with the other. Seriously, who would do that?! (um, yeah...)
Adding the cord
This is modeled to be used with Apple's default lightning cable. However, to get it to make the turn you'll need to carefully cut off the cord stress relief rubber.
Please note that the cable will not just slip merrily into the base (depending on the shrinkage of your particular filament). You need to use a file to hollow out the hole until the connector fits very snug.
I super-glue the cord to the top of the channel, and add a big glob on the bottom of the connector to keep it in place in the dock. If your phone is in a case you'll first want to test-fit it to make sure the lightening connector sticks up off the ledge enough to sit correctly when docked.