r3aperWell, i don know how is your LED strip,
1. is it single +/- for multiple LED or
2. separate +/- for each LED? how many LED in total?
For pic 1 (555 timer + counter 4017 IC]
This one is counter circuit, 555 is timer and output clock to trigger 4017 switching. each output goes high in turn. So is not suitable if ur LED strip is (1). Output voltage will follow more or less same as Vcc input, means if u provide 6V, output is around 5-6V max only, so this voltage enough to power ur LED or not? i dun think so.
For pic 2 (fading circuit)
Again this one is 555 timer + switching transistor which C1 (100uF) act as a main 'fading effect' component to this circuit. C1 provide current is exponential rate so that the transistor ON-OFF exponentially, and LED will looks like has 'fading effect'.
Voltage supply is not a crucial part for this circuit, as we have a lot of DC-DC converter AKA voltage regulator (3 pins like trans too) convert from higher voltage to let say 5V (safe operating voltage for IC and LED). But the most crucial thing is u must know the current consumption and power consumption of ur LED, forward voltage drop of LED, connection o LED (series or parallel) which in turn affect ur component selection. I dare to say 4017 alone will not be able to provide such high power for ur LED strip and will burn if certain current exceeded, same as transistor as well. So don simply plug and play if u dun have electronic background, and sorry to say that, to guide you by words alone is simply too difficult for me.