How involved is eyelid surgery and how much recovery time is needed?

Recovery Time After Eyelid Surgery - Recovery time after Blepharoplasty is usually 7-10 days. Blepharoplasty is done commonly with a lower facelift if you have facial fat atrophy and central sagging. This should be done in the hands of a Board Certified Plastic Surgeon with expertise in Facial Rejuvenation and has an understanding of the science of aging of the face.

Your question is more related to an entire facial rejuvenation vs. just an eyelid procedure. So to break down your question -
The extra skin on your eyelids can be removed safely. It also often involves removing or repositioning "extra" fat around your eyelids. Sutures are usually removed in one week. The swelling subsides rapidly initially and the final result may take 6-12 months.
In terms of your other concerns, this would require a "face lift" depending on your expectations. There are some non-invasive methods of neck skin tightening but they do not compare consistently with the results of a surgical procedure. As a board certified plastic surgeon in San Francisco, I have been very interested in reducing the recovery time of a face lift procedure. The recovery process, which incorporates the reduction in bruising and swelling after surgery has been reduced in my patients by using a laser to dissect the tissue at the time of the face lift procedure vs. scissors or knife. The laser seals blood vessels as they are divided, which results in less initial post operative bruising. The less bruising initially, the shorter the total recovery period. Other important items factor into one's recovery period - the patient's age, health, number of procedures performed during the surgery and the post operative protocol. Keeping one's head elevated above their heart, initial cooling, resting vs. trying to return to normal activities immediately can factor into the length of the recovery period.

Droopy eyelids can mean excess upper eyelid skin (fairly straight forward) or actual problems with incomplete opening of the upper eyelids (more involved). Combining this with the jowls and loose neck skin can require a comprehensive approach so that the end result is balanced and natural. There are many approaches to these problems depending upon the severity (the amount of looseness). Consult with members of the American Board of Plastic Surgery, view some before and after results, and you will be in excellent hands. Go with the surgeon and the approach that makes the most sense and feels most comfortable for you.

“Droopy eyelids” could be a couple of different things. If you are referring to bags under the eyes, this can be treated by a lower eyelid blepharoplasty. This is a relatively straightforward procedure, commonly done as an outpatient, sometimes even under local anesthesia. If the droopiness is a relaxation of the lower eyelid away from the eyeball then a slightly more involved procedure is required but this too is commonly done as an outpatient.
The treatment of sagging jowls and loose neck skin will likely require a facelift. This is commonly (but not always) done under general anesthesia. This procedure can easily be combined with the lower eyelid surgery. Your overall health status and care for your recovery will determine whether this can reasonably be done as an outpatient or whether a night’s stay in the hospital is more appropriate. Recovery from a facelift is typically 10-14 days.
For the best results seek the consultation of a plastic surgeon certified by the American Board of Plastic Surgery. They have a website listing all the certified plastic surgeons. Members of the American Society of Aesthetic Plastic Surgery will all be board certified in plastic surgery and have demonstrated an interest and competence in cosmetic plastic surgery as well.