Which type of eyelid surgery? (Photo)

You can relax. Really no need for expensive, invasive surgeries that risk infection, scarring and engender significant post-treatment downtime. The kind of issue seen in the photo is one that is routinely treated with the appropriate HA filler in active cosmetic dermatology practices practically on a daily basis.
The photo shows evidence of volume deficit in the cheeks and since the upper cheeks serve as an important support for the under-eye region, volume deficit in the cheeks typically results in infraorbital hollows and tear troughs making the eyes look very tired.
The appropriate use of an HA volumizing filler for the upper cheeks typically results in immediate improvement that evokes a "Wow!" response and engenders little to no significant downtime.
So before jumping into unnecessary surgery with its expense and risks, you would be wise to consult with an experienced, board certified cosmetic dermatologist filler expert and relax.

You may have ptosis of you upper eyelids. They should be evaluated by an experienced surgeon in ptosis repair. Lower lid Blepharoplasty usually does not correct hollows under eyes unless you have excess fat that can be repaired. Filler and fat transfer may be your best options for lower lids. Or you can simply use makeup and avoid surgery altogether.