If you want to go the suboptimal route and use the staff one handed with a multiclass or feat usage for a secondary stat to attack with I say more power to ya.
As long as you as a player realize you’ll not (nor should you) be as viable as an dedicated martial character (or an optimized bladesinger) in melee combat.
personally I’d go the monk route but with shillelagh stats- since you can’t use the martial arts if you’re wearing light armor, you’re going to need to have a high wisdom regardless if you want to have a halfway decent AC.
you’re still throwing points at a stat you don’t really care much about except to twirl your stick, but at least you don’t need to waste an action to make it happen.
Yeah, you really could do worse than starting as a monk with a staff and magic initiate feat.
You can reasonably pick shilelagh, guidance and goodberry and you have a solid level 1 character with a lot of sustain. You can cast the goodberries before going to bed, so you will probably have 20 of them on the next day.
shillelagh will increase the damage to 1d8, even if you only use one hand later on. In the first few levels you are also better served by just doing the offhand attack instead of using booming blade or greenflame blade.
If you are a wood elf, wood elf magic would be an even better feat. A druid cantrip and pass without trace. One of the best level 2 spells you can find. You are also 35ft fast and can cast longstrider once per day for free.
With standard array you can now easily afford 16 Dex, 15 Int, 13 Wis and 13 Con and if you do point buy even more.