Bigger isn't aways better. Dispite what you may have heard having a 3" cat back pipe on a 4 cyl Honda isn't a good idea, unless it's making over 300hp. If the pipe diameter is too large you then run the risk of losing horsepower. No back pressure causes a loss of low end torque. Some back pressure is required. Your goal is to increase the flow, without robbing the engine of the power gain. 

An exhaust that creates too much back pressure is called a Restrictive Exhaust. Most OEM exhaust are build as a restrictive type with cost and gas ecomony in mind. A restrictive exhaust hampers performance in two ways. One is that the engine has to work harder to push out the exhaust gases from the cylinders. Second is the engine has left over gases in the camber which then get diluted with new incoming air and fuel mixtures. This can help gas mileage, but performance suffers.

Yet, backpressure is needed to remove gases from the engine. Back pressure creates something of a suction to help remove spent gases when it isn't too restrictive. Too much backpressure and it can't all escape, too little and the engine will pull it back in through the exhaust valves when open. It's a balance your trying to achieve as you increase the power of the engine.

It is usually associated with a popping or burble noise coming from the exhaust, not a backfire. You should expect properly tuned engine to burble or pop when the throttle is close from a high RPM. Think of a top fuel dragster and how the engine at idle makes the popping noise. That engine is creating a lot of backpressure. That is also the reason for the short open headers and with the remaining small amount of back pressure the gases are removed easily. If your car is making loud pops under hard accleration/decleration then that is backfiring.

Backfiring is not a good thing. We've all heard of a car being called a fart can. It's due to the unburnt fuel getting into the exhaust system and then it is being ignited. Commonly it's a small air leak in the exhaust system connections. It can also be due to a lean air fuel mixture or it could even be related to the ignition system. The ignition sequence could be off, or the plug wires worn, and the coils themselves could be bad.

If you plan to upgrade your exhaust then you should look for a system that is .25 to .5 inches larger than the existing stock exhaust piping. This will give you the best increase. Also to consider is what RPM will your car or truck operate at, most of the time. A exhaust pipe with a smaller diameter will produce more low to mid range RPM torque, where as a larger pipe diameter will increase mid to high range RPM torque.

Below is a chart that will help you also determine what diameter is needed depending on the horsepower your engine creates.

Mufflers and Resonators:

A free flow muffler can help the removal of exhaust gases, but sound increases. You can use a resonator or spirl flow gas pack muffler to help reduce sound before the muffler. I've ran a 4 cyl car with just two gas pack mufflers, which helped a lot in performance, but created little more noise than a normal burble.

A muffler can be straight through or have an S-turn. Just make sure the pipe diameter of the in/out is upgraded to size of the piping used. The gases are NOT trapped by an S-turn muffler. Sound is trapped. Once you nail the throttle everyone will know, but before that the normal sound of the car won't attract much of the wrong kind attention, usually from law enforcement.