We regularly build sound competition vehicles @ our shop (mine hits 141dB at the moment) and have NEVER used a cap nor seen many at any competitions. If you can only run one battery, an Optima Deep Cycle Battery (Yellow or Blue Top) would be the best as it can take more abuse, higher current draws and total discharges than a Red Top. And then a higher output alternator to keep it full.

Also, many 2200 watt amp specs are only a transient measurement and not RMS - check the fuses and I'll be you find no more than 2 30 or 40 amp fuses - that is only good for 720 watts RMS.
http://www.the12volt.com/ohm/page2.asp

A second battery would be the next thing to do after the alternator - the 1000W and 1400W RMS amps we use require a second battery or we don't install them. Low voltage/current is the leading cause of amp failure.

I use a commercial Yellow Top (1125 Cranking Amps) for starting and when driving (it turns off when in Accessory position so I can always start the vehicle) and a regular Yellow Top (870 Cranking Amps) for running the stereo with the engine off and adding to the front battery when the engine is running. And all power handling / ground wire under the hood and to the amps has been upgraded to 1/0 cable. The ML came with a 150 Amp Alternator but more would be better....