In most cases, the stock-size battery is correct, and that's what you should stick with.
A smaller battery is likely to fail you sooner, unless you live somewhere without a winter (Hilo?).
A larger battery is an extra expense, extra toxins, extra weight, and won't give you dramatically longer life.
CCA (cold cranking amps) is the main thing to pay attention to. This is a measure of how much current the battery can provide at 0 deg F, as @Pangea points out. Batteries work better when they are warm, so the colder it gets, the less current it can provide.
Starting an engine requires a lot of current, over a very short time. Meanwhile, cold engines are harder to start, requiring more power to get them going.
As batteries age, their internal resistance increases, reducing CCA. Total capacity decreases at the same time. This is why a newer battery can start your car in any weather, even if you leave the headlights on overnight, while an old battery might only start the car when fully charged, in good weather.
Starter batteries are optimized for short-duration, high-current draws, followed immediately by recharging. They are built with thinner plates with more surface area, which speeds up the chemical reactions that release the energy. If you draw them down to 1/2 charge, and then leave them like that for a while, hard crystals will form on the plates, which won't re-desolve easily on recharging. That reduces capacity and CCA over time. So, keep your starter battery fully charged, and avoid dropping below 80% during non-starter usage.
(Deep-cycle batteries, like on golf carts, fork lifts, some boats, some RVs are able to tolerate being discharged deeper and left that way longer than starter batteries, but they really don't like a high-current draw like for starting an engine. Best to draw on them gently, and never below 50% if you can help it.)
So, a regular car battery is not a good device for running appliances for a long time, without the engine running. However, a stock car stereo doesn't draw much current, so you can probably get away with it for a while without a problem. But if you leave it on all night, you may drain your starter battery enough to damage it.
Increasing your battery size will allow you to run those appliances for a little longer, but it's still not the right technology.
In an RV or boat, you have a starter battery and a separate "house" battery, which is deep-cycle. Then use a battery isolator switch to use only the starter to start, then recharge it, then recharge the house battery from the alternator. (You can also use the house battery to assist the starter when the starter battery is low.) Some people build these in to their cars if they have really big stereos, or a small camping setup with fridge in a van or pick-up camper. You can learn more from RV articles, like this one: http://www.phrannie.org/battery.html