32k on a "328" type arduino such as a nano v.3 is enough for it to upload more program than compiles from 10+ pages of source code c (which being edited on your pc or other external device can be typically >50kb in notepad)
I don't know if you remember the BBC micro. That had 32k total.
Also, it had "himem" and "lowmem" places to keep the basic editor separate from the compiled running instruction.
Arduino does not have flexibility to move that boundary.
32k is the size of "program memory" to contain the binary compiled on your pc and uploaded to it.
That tends to be about as compact as the proffessionally compacted assembler of a game on a BBC micro.
Think "Repton" or "Elite" for how much information that can hold.
Also note the size of "SRAM" data memory on the arduino, which is a separate section of the chip, for which you cannot just move a "Highmem" partitionmarker like on the beeb. On my "328" that is 2kb SRAM, and I keep a careful watch on it during development using functions copied from (look up memoryFree() ). SRAM is where you store normal data in use in your program, and I try quite hard to keep that as small as sensible, to leave more room for future additions. Also I'm curious about that. Just the library to use Serial.print and libraries to display to an lcd screen can fill 500bytes before you have started programming anything much. Still, it is a lot better than making room for BBC Mode 2 Graphics, if you remember that.
You probably wont use EEPROM, which is as good as having a built-in tape drive as a system-on-a-chip. That has 1k of capacity, and for example can hold your "if lost, please return to" message, calibration constants of any sensors which you have made, and stuff like that to be accessed very occasionally.
So, your thoughts about memory are I think, about right. The unit which you were thinking of getting is indeed way overkill for many applications. Depending on what uses you have for it, you might find a "328" based arduino to be about right for quite a lot of things. And they are so cheap that you can always buy an extra nano v.3, a bit of pinboard, a bag of LED's, assorded resistors (I find 10k to be the single most used value), and some bits of single strand wire. I quite like 2N7000 nfet because those switch cleanly a fair lot of mA from a 10k resistor from arduino digital_out to gate.
For your particular choice of writing to an LED array, I am confident that a "328" arduino is plenty.
You'd have enough to write your "Hello Macnerd" to an lcd too, if you got one and figured out how to make libraries findable to your IDE.
SRAM of up to 2k, being cautious knock off 1k for diagnostic program messages and extra bits, could leave you with at last a k.
Being sensible about bitpacking, for example using digitalWrite( (bytestore[x][y]>>z)&1 ) it has about enough room for 32x32x8 led states max.
Your decision depends on whether that is enough.
I also have a "168" based smaller original arduino, presently monitoring a few battery and solar panel voltages.
You don't need to go that small in 2014.
