Best Peels for Brown Spots and Small Seborrheic Keratoses?

TCA peels can be used effectively to control brown spots  and superficial seborrheic keratoses on your face and  other area. . However different areas of the body have to be treated differently because the skin is much thinner over the hands either less coats or a less strength TCA is required than say your arms where the skin is thicker. It is key to make sure your Plastic Surgeon or Dermatologist has lots of experience to prevent complications; For example, it is important to pre-treat with some prescription creams first. This is to prevent brown spots following a TCA or any other peel, laser or deep dermabrasion procedure. This is  called post inflammatory hyperpigmentation. The inflammation part is a normal part of the healing process but unfortunately you are sensitive to the sun which is what causes it. Ideally your doctor would have pre-treated your skin some weeks before your treatment with Retin A, 4% hydroquinone, and a strong SPF sunscreen and/or other agents to prevent this from happening. As soon as you are given permission you would again start these products plus perhaps Kogic acid and use them for some time. Once they are established it is more difficult to get rid of. The same treatment can be done again but this time use products recommended by your doctor before and after. If these were not suggested you might want to seek another plastic surgeon or dermatologist to treat you.

Various lasers are also effective for this purpose.

Given that you are fair and likely have sun damage over the years, you would do well with a medium depth peel such as 35% TCA. Laser resurfacing with Erbium laser or even IPL (Intense Pulse Light) treatments would give you the desired result. You can also use a prescription cream called Triluma for the spots.
You should consult a dermatologist to see if you have any actinic keratosis which looks like seborrhic keratosis but can be pre cancerous. In that case you could treat your face with either Aldara or 5-FU.
Along with all this don't forget the most important thing; daily sunscreen. You could potentially live for another 50 years and you need to start protecting your skin.
Regards