Okay, im going to repeat a few things just to make sure everything is covered. Depending on your mileage, especially if its high, the catalytic converters, CAT's, could become clogged. Air can't escape the system as quickly and decreases performance and fuel economy.
Decatting a car, thus cutting out the two CAT's in the exhaust, and if applicable the two cats in the branches, and replacing them with straight pipes or resonators will free up the air to flow through faster thus increasing performance and fuel economy. They range from R350 - R1500 depending on if you are only removing the CAT's in the exhaust, or the CAT's in the branches as well, and if you are replacing them with straight pipes or resonators.
If you replace them with straight pipes, which are just two normal steel or stainless steel pipes, you will get that distinct raspy M3 sound and the car may be a little bit louder. If you replace it with resonators which are little boxes, you will not really get that raspy sound but a deeper tone and bit louder.
NOW, the reason why some people say your car won't be more economical is actually just a joke as you will only get that nice sound when the car goes beyond 3000RPM. Thus you will be hammering your car to get the sound every time. But if you drive like you always do you will improve fuel economy with a decat.
You must choose between a full exhaust and a decat. As a new exhaust will in effect replace your entire exhaust and the CATs. Supplementary to that if you have CAT's in the branches you can decat the branch and then you can add a CAI (Cold Air Induction).
When all this is done you HAVE to get the car chipped. You have now replaced some parts and the car knows its there but it its not using the mods effectively with the standard ECU system. Thus the chip or flash of the standard ECU will make everything work together in perfect harmony at optimal performance.
So costs:
Decat R350 - R1500
Exhaust R2500-R3500
CAI R1500 - R2500
Chip R2800-R3500
So now you see why people often just start with a decat and work from there because its the cheapest mod you see results with