What should someone do who has recently started praying, only memorizes a few short surahs, repeats them in every obligatory and supererogatory prayer, and cannot memorize more due to their circumstances and age?

One must hasten to repent, observe prayers regularly, increase acts of seeking forgiveness (istighfar) and good deeds, and make up missed prayers in order if their number is known, or continue making them up until one is reasonably certain of having cleared their debt if their number is unknown.

As for memorizing the Holy Quran, it is a communal obligation (fard kifayah). One can join memorization centers or listen to reciters and commit to memorizing a small portion daily.