Can be done yourself, but you need the correct battery (deep cycle and stop/start ignition optimized). Then you put the car into learning/re-calibration mode.
Search the forums, I learnt that all here.
I'm not sure what the start-stop system is, so my comments below do not reflect this option.
I just replaced the battery in my 2016 CX-3 GT yesterday because it was noticeably slower to crank the engine over in the mornings. The replacement battery on the CDN version is a Group 35 (this represents the overall dimensions of the battery case), with a minimum of 520 (CCA) cold cranking amps. I replaced mine with a slightly higher rated battery with 640 CCA, because Canada!
I've replaced batteries in every vehicle I have ever owned, plus a few in my kids vehicles so it's not a difficult job. Because this vehicle has many electronic options that I've never had before, I decided to watch a youtube video and learned that if you connect a battery tender to the terminal clamps BEFORE you remove them from the battery, you will not loose your radio presets. It also allows other information stored in the onboard computers to be retained. Apparently, if the radio looses power it might not work until reset with a code. By using the battery tender I was able to replace the battery without any problem and everything works as it did before.
It is an easy job and all you need is a 10mm deep socket, since the bolts on the battery hold down clamp and terminal cables are the same size. Remember when removing the cables from the battery it's negative first, then positive. When you reinstall attach the positive first, then negative.
After looking online I understand what the Mazda iStop system is and I'm glad I don't have that on my car. It sounds like it would be annoying and doesn't really save that much fuel.
Back to this thread, since iStop doesn't use the starter motor to restart the engine, I'm not sure how this option would require a different battery. In this case the OP should check with the dealer to be sure to get the proper battery replacement.