Most switches from GE and Leviton these days are three-way compatible/ready, but you need to use the companion switch of the same brand and product family (I think GE even has a package with the two together in the same box).
However, you should not do this yourself. If you are asking here, you do not know what you need to know to do this job safely, and you need to hire a licensed electrician. Practically speaking, wire color means nothing; while there are standards and conventions, there is no telling if your home was wired to those from the start, or if work done since it was built did not alter the original conditions. Nobody here can safely advise you on the current purpose of each of these wires; it would take testing with a meter or other devices to ascertain how the wires are being used, and then, which terminals on the new switch would be connected to which wires on each end. The voltages present here can, and given the opportunity will kill you and/or burn your home down. The electrician would also be able to ascertain if a neutral is present for the new switch, which many require, and many older homes in North America were built without. If that's the case, you may need to find a switch that does not require a neutral (these are available); so consult the electrician before buying any replacement products.