Depends on the space available on the table. Usually Edifier R1600T III would be just right, though quite big for multimedia speaker (since its a full blown stereo speaker system, and not your typical 2.1 type speaker system with small/tiny satellites)... 

Try Edifier M3400. As always, try auditioning/testing them and see which one suits your listening preferences...

Should be relatively same (due to having similar satellites) although there are some differences especially when it comes to subwoofer wattage (18WRMS on the M3400 versus 16WRMS on the P3080M). Anyway, how does it sound to your ears? Is it an upgrade/improvement compared to your previous speakers?

Should be Edifier M1360 for better sound quality. As for the Logitech Z213, the satellites can sound rather thin (as those drivers looks to be the same type of drivers as found in portable speaker systems)...