I would recommend working on your speaker placement first. They should be off the rear wall by at least a foot or two. I would also recommend placing them on old milk crates (or something similar) so they are not directly on the floor. If possible, spread them out in some sort of symmetrical fashion along a wall, pointed in slightly (not facing each other on opposite sides of the room). If you want to buy something, start with your player, then work your way down the signal path. It all starts with your source. I've witnessed a decent front end and new cables transform old-school systems like yours on multiple occasions. I have to disagree with BC regarding speaker replacement. I think your speakers are good enough to be taken along for the ride, at least for a while.
Chris