Hi,
Congrats. I started with 35mm and an FTb and 50mm lens.
The meter is the only thing that needs a battery on an FTb. Not so on the A-1, however. You should be able to get the battery for the A-1 at most places that have a good selection of batteries, however, the FTb's 625 battery is no longer made exactly the way it was made back then. There is a Wein cell that you can get for it that is of the proper voltage (1.35V), but they are relatively expensive and don't last a long time. Also, you can get the alkaline version of the old battery, but the voltage is wrong, so you need to compensate for this, or have the camera tinkered with by a repair person to read accurately with the alkalines. I had mine calibrated to commonly available and dirt cheap 1.4V 675 hearing aid batteries and they work fine. You just wrap the small 675 in a rubber o ring or a split metal ring and this takes up the empty space.
You can shoot your FTb without the meter, however, and IMHO, it is better that you learn to shoot based on exposure guides rather than on your meter. Meters are only guides, and in order to operate them properly, you need to have a thorough understanding of what they are actually telling you. You can learn this fairly easily, but IMO should just go out and shoot for a while without worrying about too much of the technical stuff.
IMO, it is easier for a beginner to learn using the sunny 16 rule. This is known as BDE (Basic Daylight Exposure), and you simply make adjustments off of it for different levels of light. For instance, BDE is: when shutter speed equals film speed, in CLEAR and BRIGHT sun, use f/16. This does not mean you have to use f/16, of course. You could use f/11 at one shutter speed faster than your film speed, or f/8 at two shutter speeds faster than your film speed, etc. For shady shade, I usually open up to f/4. For brighter shade, f/5.6, etc. The film boxes usually have decent guides to get you started.