I paid $13 for a Logitech 2.1 system on clearance to use with a TV. Wasn't expecting much but the improvement was stunning. Says more about TV speakers than a $13 powered system though.
The vast majority of LCD TVs have horrible sound. Slimness is everything so they hide piezo type speakers in the base, back etc.
A basic Logitech or Edifier type 2.1 system with say 3/4" mid-woofers and a 5-6" subwoofer is a substantial increase in plain vocal legibility alone.
My other place has a TV in every room and I have been able to get free or close to free 2.1 systems on every one of them...
IMO this place has Chinese digital stereo amps and Chinese DACs covered... there's no greater resource on the internet than this place on that subject... which I find to be ironic. You can fill in some gaps with all the other Youtube folks who love Chinese gear like Randy and Williston.
You can get a $100 amp and a $100 dac that has performance literally impossible a decade ago.
HOWEVER there's still a gap and that's speakers... I personally wont ever buy anything less than 6"... there's no point... you dont save much space and you lose so much... "body"... and so here you probably should focus your efforts.
Find a good set of 6" plus bookshelf speakers... these three things would get you pretty far in.
Let us not get into subwoofers because then you get into crossovers and that's messy.
I think a good three piece setup would satisfy most. I'm not sure the Chinese are there yet with a 'decent' digital integrated amp that isnt too much money.
The Sabaj A30a is a popular product here but its quite expensive. I would love to see a $250 digital integrated with analog inputs and all the usual features and a robust 75w or so.