You won't need any current limiting for the fan. Its a motor and builds up something called back EMF to limit the current from shorting out. That's a wiki page you can look up, and a very broad topic. With your fan's configured in series like that, they will operate at 6 volts, or approximately half speed.
I also think your 3 amp power supply won't be enough.
Doing a little math I get:
LED strands x5 @ 700mA each = 3.5 Amps
Fan x2 6V @ 150mA (a guess as it is configured in series) = 150mA
Mind you, every LED posting I have seen, the user ends up lowering their power output to 20-30% of maximum so they don't create an algae farm. But in order to operate at full power, you would need 3.65 amps. I would settle on a 4 amp power supply, or a 7.5 amp with the intention of adding more LED strings in the future. I don't think the cost would be that different.
The pre-packaged variable power supplies are not a bad idea. If you don't have the supplies, getting the decoupling caps for 7805's can be a pain, and protoboard for soldering is expensive (at least on digikey). Another advantage is you could also dial it in for the exact voltage that you want. You are paying more, but you don't have to get into that engineering level of detail. The trade off might be worth it. This could be used to power the fans and arduino, but a LM7812 would work as well.
In this application, you don't need the isolation that the transformer provides. To save yourself a headache in troubleshooting, I would tie the ground of the individual LED strands, violet, cyan etc. to the common ground of the circuit. That is if you decide to go with the transformers.