center vs. "phantom center" is purely a personal choice. Even in very entry level "budget" systems I have helped set up for others, the addition of the center channel speaker greatly enhances the "surround" experience by fixing the on-screen vocal audio to the position of the TV itself.
With the extremely agressive pricing currently available on the Polk Monitor towers and CS center channel speakers, you can easily fit the front 3 speakers into the top end of the OP's budget (or stretch it slightly

) and end up with an outstanding "budget" system that sounds much more "expensive" than it was.