An experienced plastic surgeon or maybe an oculoplastic surgeon should be able to evaluate your entire face and offer treatment options. It is very important to look beyond the lids and evaluate the brow position in situations such as yours because a browlift (forehead lift) may be the better way to deal with most of the excess skin and in addition treat low eyebrows as well as forehead wrinkles, loss of brow arch shape, and active frown lines. Excess bulging fat in the lids however requires a blepharoplasty. Sometimes both a brow lift and a blepharoplasty are needed to get maximum results.
Look in the mirror and use four fingers to raise your brow to a reasonable height (so you don't look surprised) and see how your eyelids look.
Lower lid surgery may or may not require skin removal but surgeons have become more conservative with skin removal and often wrinkled skin is better treated with a CO2 LASER rather than removal. The lower lid puffiness is usually treated by repositioning the fat down lower in the lid to fill in the hollowed/ shadowed area (tear trough) rather than removal. Sometime the entire cheek must also be lifted to further fill in the tear trough and redefine the cheek and the lid-cheek junction.
The veins can rarely be removed by laser but can be surgically stripped if they are large enough.
You can see that a full evaluation should include an overall look at your face and a discussion of these possibilities..