I still suggest a high-quality battery. You will never regret a good battery. As for the stereo, do the numbers:

To calculate how many amps your stereo is going to need you do:
watts = amps x volts

Your JLHD750/1 amp at continuous full power output (unlikely) takes a maximum of 750 watts. Your battery at rest is about 12 volts.

750 = amps x 12
750/12 = (amps x 12)/12
62.5 = amps

If you were continuously pushing 750 watts out of the amp, you'd need 62.5 amps to keep up. That's roughly half the capacity of the Crossfire alternator. That still leaves half the capacity of the alternator to serve other electrical components and charge the battery. That will work - just don't leave the stereo on with the car turned off and don't go getting any CIBIE World Ralley Championship light bars for your car...

You won't be doing 750 watts all the time - maybe not even for peaks. Say you only ran 400 amps (the minimum required to drive that woofer) it looks like this:

watts = amps x volts
400 = amps x 12
400/12 = (amps x 12) / 12
33.3 = amps

You are only using ~1/4 the capacity of a 120-amp alternator (Crossfire), which leaves a margin for it to charge the battery.

The battery is not the issue if your charging system can't keep up with your power needs - It's the alternator that is going to be the issue.

The math says your power needs are not substantially going to outpace your alternator. You might find that you're OK. Just don't pile too much in there or you will need to address the charging capacity of the system with a heavy-duty alternator.

For example, I knew that my other vehicle would have troubles because the 117 amp alternator was not going to do a good job keeping up with one of my attachments (a winch that draws 400 amps) so I went to a 200 amp alternator to reduce the recovery time of the battery. The winch will still sucks down the battery fast, (which is what the yellow top is for - being able to sustain repeated drains and charges).

You're not going to draw anything like that kind of power with your amp.