Hi, sorry I'm no expert, I'm just "picking the low-hanging fruit" kinda thing because it seems like at least a partially easy question
In terms of having one set of lights switch on when the other switches off, I figure you could:
-EITHER try an SPDT relay (I think...) so current would be switched between the red LEDs and the white LEDs. Not sure what sort of transistor you'd need to switch the relay (assuming you switch it electronically! You could have a mechanical timeswitch or something...), I'm afraid I don't have any experience of relays as yet
-OR make or buy a simple digital (LOGIC, not power!!) inverter circuit; then the input to the inverter can feed a power transistor for one set of LEDs, whilst the output from the inverter can feed another power transistor for the other set of LEDs. That way only one set would be running at once. Depending on various details, you might want to use darlington connections to feed the output transistors. It wouldn't hurt but it's a few pence more money and a tiny bit more soldering
Not sure about the best way to handle the timing for such a thing, I'm sure someone else can come up with something though. All I can think of is a microcontroller (eg a PIC or similar) or a 555 timer. The PIC could work very well but would be a bit involved; the 555 would *probably* be cheap and easy to make something bad but hard to make something good I think.
Incidentally, if you're using multiple LEDs in each set, you should probably wire each set in *series* (ie + to -, anode-to-cathode, long-lead to short-lead, you get the idea), and then drive them with a constant current (of approx 20mA), RATHER THAN trying to wire them all in parallel (ie, all the anodes connected together and all the cathodes connected together) and then having a resistor and giving them a constant voltage.
If you do go the route of using the LEDs in parallel, I think you might get away with it if you did it using a separate resistor for each LED, but I'm not sure how to explain that clearly, sorry
If I get the chance later and you don't get what I mean about some of that, I might bash out a simple diagram to show you what I mean. Or someone smarter than me might say something more useful meantime