There are some advantages to a modem and router combo. You don't have to worry about as many cords. You only need one plug for power instead of two. The combo units also tend to be around the same price as a modem and router, if not cheaper. If looks or space is a primary concern for you, then a combo device may be exactly what you need. However, make sure that you understand what the device is capable of and the compromises it makes.
Modem and router combos generally don't perform as well as their stand-alone counterparts. Commonly, the router side of the combo just doesn't have the signal strength or feature set to compete with a stand-alone router. Essentially, it's trying to jam too much stuff into one box.
Knowing your internet’s DOCSIS version will greatly help you purchase a new cable modem and router combo because it dictates what model of hardware you should buy. Also, cable internet companies such as Charter often have a list of hardware that is compatible with their system. Be sure to check out your ISP’s website before deciding on anything.