Quick question: You say that you're playing tt direct into the soundbar - does the tt have a built in phonostage? If not, then that would go some way to explaining why it sounds bad.
If you don't get a tt with a built in phonostage then you'll need to factor that into your budget (better tables tend not to have them built in).
I'd avoid the Crosley - it won't help you preserve those nice records that you'll be spending your money on, since the stylus is set to weigh
very heavily in the groove and can't be changed, and the tonearm geometry is such that the stylus alignment will be more off than it should be, so won't sound great.
As for alternatives, with your budget I'd recommend going vintage/secondhand - your $250 will go a lot further this way.
edit
As an example, something like the
Technics SL-1500 would do a fine job.