rl

A few quick thoughts from a non-expert:

• The concept is sound. Many professional astro spectrometers are fed from an optic fibre because the spectrometer can be located statically in an airconditioned room where it is much more stable thus can detect smaller velocity changes in the doppler component. 
• Your spectrum looks good for a single shot. If you want less noise, can you stack them in the same way as standard astrophotography?
• How are you going to ensure the primary image of the star always hits the optic fibre accurately? You may need some sort of diagonal-with -a- hole arrangement. Can you arrange a guide camera with PHD2?
• Optic fibres have a limit on how steep the entrance cone can be before light is lost..I think it's referred to as "etendue" and basically refers to how fast your scope is. The spot size scales with the scope's f-ratio. Slower is probably better providing the larger spot size still fits inside the fibre. But slower scopes for a fixed aperture have more focal length and are thus harder to guide...there will be a bunch of tradeoffs here. 
• Is it worth starting on the sun just because there is so much light available you could just mount the fibre in the expanded beam behind an eyepiece. Usual safety caveats apply... at least you could get the spectrometer end functional first and in the daytime. You might get away with just pointing the fibre end at the sun if the exposures are made long enough.
• Are you expanding out the beam at the spectrometer end with a collimation lens before the grating, and using a lens after to focus on to your camera? If so, f-ratio considerations apply again. One plus is that you get to scale the image to your pixel size. The fibre diameter becomes your slit, in effect, and the image of that slit will determine your resolution?
• Not sure of the blaze on a simple transmission grating. How much of the light is wasted in the zero-th order spectrum? (i.e straight through). Might you get a better signal-to-noise ratio with a grating with a blaze angle optimized for a 1st order spectrum?
• Are you using a colour camera (pretty but inefficient) or a monochrome? I have bought up a small fleet of old secondhand Atik 16ICs for this purpose; they are cheap, cooled and have about the right number of pixels without overkill, keeping the file sizes small.
• There are a few books available on amateur spectroscopy, the titles of which all escape my ageing grey matter at this instant. Several delve into the basic principles in some detail without being overly complicated. Might be worth a read checking the concept and the maths before you commit too much time going down a dead-end. I will look them out later on if you need further direction...

Good luck..spectroscopy is fun! Especially when you get your first result off a nova and calculate the expansion velocity...

Hopefully those more qualified than myself will chime in...

RL