The numbers you care about are "voltage" and "current" (and perhaps how long the power source would last, in the case of a battery). Voltage is measured in volts, and current in ampere (technically its the "maximum current flow").
You need a 5V 1.2A power supply for a PI (that's five volts, 1.2 ampere). For normal use 1A would also do great (I never found the requirement for 1.2A, even with multimedia).
10A is A LOT of current, way more than the PI can handle. It will work, just like a 1A supply, but its just an overkill and you would be wasting money.
Your battery, which gives out 5V and 1A is perfectly fine. But it won't be enough power to power that LED array.
You need to see how much current your LED array demands, and add that to the 1A the PI is going to take.
DO NOT plug anything that is above 5V, you could fry the PI. A higher voltage is BAD. A higher Ampare is good, but beyond 1.2A is not going to effect anything, unless you want to plug more devices at the same time, to that power source, then you need more current to go between them.
One more tip: A power supply should be regulated, so jumps in the power supply don't mean jumps in how many volts they are giving to the device. Many cheap power supplies (ones from ebay and such) do not have those regulators and give out 6V and not 5V as it says on their casing. Avoid "too good to be true" prices, there is a reason they are that cheap.