Hi Mike
Yes, I think that a 12V 12A.hr battery should be more than adequate - but leave buying the battery until you are ready to put the hull into the water. then if you find you need more ballast you can buy a bigger battery. For my 2 AZIZ kits I bought the biggest battery that would fit through the access hole in the foredeck.
Selection of ESCs for a particular job can be tricky if you don't understand what the numbers mean - and that includes many hobby shop dealers. For my first AZIZ I used the Action P94, rated 20A on each channel. But when I measured the actual motor current, at around 3A each, for my next AZIZ I used the P94 Lite, rated 10A per channel - and then installed 7.5A fuses in a motor lead from the ESC to the motor. So the motor is protected from overload (if the props get fouled with weed, or similar), the ESC is protected, and I saved a couple of bucks.
For my bow thrusters I have used the Action P93 multi-function controller. But if your hull has both bow and stern thrusters then I'd be tempted to look at the P94 (lite); if I remember correctly this can change from spinning the boat, to translating sideways, with a simple "blip" on the throttle stick.
I have noticed on this forum that many members use motors much bigger than those I have used in my AZIZ's, and for them bigger ESCs are both appropriate and necessary. But for a tug around 1000 - 1200 mm or so they are not usually necessary. (By the way, what size props & nozzles are you using on your Alpine - that will make a difference).
Des.