A lighter eye serum is great for daytime, while a more dense, hydrating cream is a good bet for nighttime.
You might also want to shop according to your concerns: dark circles benefit from the active niacinamide; under-eye bags from caffeine; and wrinkles from peptides and growth factors.
$: The Ordinary Caffeine Eye Serum
$$: Osea Ocean Eyes; 100 Percent Pure Coffee Bean Eye Cream [caffeine]; DIME Beauty Luminosity Serum [niacinamide]
$$$: Tata Harper Elixir Vitae
PM: heavier for more nourishment
$: Acure Ultra Hydrating Eye Cream
$$: 100 Percent Pure Multi Vitamin + Antioxidants; Beautycounter Countertime Ultra Renewal Eye Cream; Bluelene Eye Cream
$$$: Power Step REGENERATE Chara Omni cream [peptides & growth factors]