I always use the table on page 38 of the DMG when bringing new PCs in at any time other than the beginning of a campaign. I also let them use the gold to "buy" magic items:
Common - 50 gp
Uncommon - 500 gp
Rare - 5,000 gp
That's pretty much what I do. I let 5th level PCs start with 1 Uncommon item + 100gp.
I don't let new PCs start above 8th level, but when I did (running an AP) I used the DMG table Medium Magic settings.
I'd generally suggest Tier 2 PCs should have an Uncommon item, Tier 3 a Rare & 2 Uncommon, Tier 4 a Very Rare, 2 Rare, and 3 Uncommon would work (watch the attunement limit - there are several handy non-attunement Uncommons useful at all levels). But 5e item rarity allocation is very haphazard so best to use a curated list.
My Uncommon Items list for starting level 5 PCs:
+1 weapon, +1 shield, goggles of night 60' darkvision, bag of holding, cloak of elvenkind, Boots of Striding and Springing, Gauntlets of Ogre Power STR 19, Gloves of Swimming and Climbing, Headband of Intellect INT 19, 5 doses of Keoghtom's Ointment, +1 wand of the war mage, pearl of power, helm of comprehending languages, rope of climbing, ring of mind shielding, lantern of revealing.