At that budget you can get something noticeably better that he TV built-in sound but still pretty compromised so I would likely just get one from the same brand as the TV (assuming it’s a big name brand) and look for a deal in store.
Def demo it first if you can to (and read reviews online), the first one I ever bought I think I paid £400 (but that did include a Blue-ray player) and whilst the sound was OK in general it was horrible with dialogue in films and any background noise going on, the background sound would just overwhelm the dialogue (and this isn’t related to the hearing thread :p ). Unfortunately there was no way to change the pre-set balance etc.
I spent a bit more when I replaced it and there’s various modes (sport, theatre, news etc.) as well as the option to customise things, I’m far from an audiophile but it makes a big difference.