Anti aging in no particular order, though retinol is most proven - retinol, vitamin C, peptides, acids, niacinamide. Not sure about vitamin c and acids so near your eyes though. Hydration and moisturiser. Superdrug do a cheap hydrating serum. Pure or something. Vichy mineral 89 is the more expensive version. Deciem do two products I hear reasonable things about. SubQ eyes and I can't remember the other one but it's under their Niod brand. La Roche Posay do a retinol eye cream. Some people think eye cream is a rip off as the skin around your eyes is no different from the rest of your face. Garden of Wisdom for vitamin C.
You might also find applying layers of hydrating toner helps. If you Google seven skins you'll get a lot of names.
Use a very gentle cleanser, oil based to take off make up, then something to take off the oil. Simple so something inexpensive. Cerave hydrating cleanser seems fine to me.
Most importantly SPF of at least 30 every day. The only thing my eyes tolerate is la roche-posay sensitive eyes and bare minerals prep step, though the latter is so runny I wonder if it's providing sufficient protection.
Cerave do a face moisturiser with niacinamide in it and I use that around my eyes no problem.
I've also used rosehip oil around my eyes no problem.
The ordinary do some peptide serums.