I'm also using the tinkercad to try to mockup the system (so I don't burn anything ), and I used a dummy code just to make things run (so you can disregard that)
The "project" can be seen in the figure attached
So far what I'm most not sure is about the ground cable connections and if I need to put a capacitor or resistors in the system, the rest I'm just almost not sure lol
Any feedback/help/boon from the gods would be greatly appreciated
It's advisable to put a series resistor in the data lines between the Arduino and the strips. Also to put an electrolytic capacitor between Vcc and GND of each strip, as close to the strip as possible. See e.g. below schematic
You should wire Vcc and GND from the power supply directly to the strips.
Is there a reason why you connect the data lines all strips to the same pin? That way you will not have an option to have different colours for the different strips. You can connect the Dout of one strip to the Din of the next strip.
Whether you need extra capacitors (those LEDs may benefit from some bulk capacitance) depends largely on your power supply, and how many LEDs you actually use.
It's recommended to have a small resistor in the data line between the Arduino and the LEDs.
Whether that has any effect in Tinkercad I don't know - it's just a simulator, not real life.
I don't know what that power supply is; rather post a link to the specs / datasheet. Did it come with the leds that you're planning to use? If so, it should be OK.