First of all congrats !! My 38 yo self en route to 40 is pleased to see we can start learning new things at 64 !! Good for you !!
If you want the perimeter LEDs to blink all at the same time, yep, you should look at an oscillator with a 555 chip. You'll need a MOSFET switch as well cause if you intend to run your 32 LEDs at 20mA, that's 640mA and the poor 555 will not handle that much !!!!
Then, if you add up the current for the other 17 LEDs, your in for a total of 980mA so you'll need, let's say, a 6V power supply rated for at least, say, 1.2A. You could use a LDO regulator to get your 5V logic supply, and a few others to get the 3.2V for the LEDs (avoiding the needs for a whole bunch of current limiting resistors). I like the MIC5209 500mA LDO series.
Like bychon said, the battery backup and remote are another story !! But it sounds fun !! I think I'll have a look at remote circuits !! I'll keep you posted !!