I have deep set eyes, I want to remove my fine lines and extra skin, would fillers or eyelid surgery be my best option? (Photos)

You have a deep tear trough.  Some HA filler placed into this will help to smooth out the lower lid.  It won't eliminate all the fine lines, but will help by adding volume.  will also help to decrease the appearance of a dark circle there.  It should last at least a year.  Make sure you go  to someone who does this regularly as it can be tricky.   

Hello and thank you for your question.  The
best advice you can receive is from an in-person consultation.  Based on
your photographs, under eyelid fillers injected into your tear trough may be a good place for you to start.   Make sure you specifically look
at before and after pictures of real patients who have had this surgery
performed by your surgeon and evaluate their results.   The most
important aspect is to find a surgeon you are comfortable with. I recommend
that you seek consultation with a qualified board-certified plastic surgeon who
can evaluate you in person.
Best wishes and good luck.
Richard G. Reish, M.D.  FACS
Harvard-trained plastic surgeon