Retweeting my Odyssey gift guide from last year, because it's classic enough not to have gone out of style.
Basic his-and-hers suggestions:
He gave two silver tubs to Menelaus,
a pair of tripods and ten pounds of gold.
His wife gave other lovely gifts for Helen:
a golden spindle and this silver basket
on wheels; the rims were finished off with gold.
Odyssey 4. 128-132.
A good choice for a man whom you have recently insulted would be a "bronze sword which has a silver handle, and a scabbard carved of ivory - a precious gift for him." (Od. 8.403-5)
Gift suggestions for the woman you hope to marry: "a splendid robe,/embroidered, with twelve brooches all of gold / pinned to the fabric" or "a necklace, finely worked in gold, /set in with amber beads that shone like sunlight" (Odyssey 18.292-296)
A simple gift list with something for everyone: a fine bronze tripod, a cauldron, or two mules, or golden cups. Od. 15. 96-97
A fun gag gift, for somebody you plan to kill and eat:
"I will kill Noman last; first I will eat
the other men. That is my gift to you!"
Od. 9. 369-70.
For a shipwrecked guest who might make a great husband for your teenage daughter:
a pound of precious gold and laundered clothes,
a tunic and a cloak.
For an avaricious guest who has recently saved your wife and son: "a silver bowl and seven pounds of gold", plus twelve jars of "sweet strong wine". 9.203-4
A gift-giving pro-tip: do not get anybody a pair of horses, unless you know for sure that they have an easy way to take them home. "You keep your lovely horses here; I cannot transport them all the way to Ithaca". Odyssey 4. 601-602.
For the awkward young man on your list, drop a little hint by gifting him a special hand-woven nightgown that he can hope to regift to his putative future wife: "the most elaborate and largest robe / that shone like starlight under all the rest". Od. 15.106-7