Regarding this, should I install the motherboard first?
Before installing the motherboard into the case, you should almost always take care of two other tasks first: installing the motherboard's custom I/O shield, and mounting the CPU and cooler. You can't put the I/O shield in place once the motherboard is mounted, so install it before locking down the mobo.
Also, does power supply affect motherboard? The motherboard is where your computer's power supply unit (PSU) is connected. It's important to buy the right PSU for your needs -- if your components need more power than the PSU can provide, it will cause the components or the motherboard to fail. But the more frequent problem for motherboards is power surges.
Simply so, should I connect my fans to power supply or motherboard?
They should all plug in to your motherboard. If your motherboard doesn't have enough slots you purchase a splitter that attaches to one of your PSU (power supply) cables. You connect case fans to the motherboard, starting with the CPU_FAN label on your motherboard to your CPU fan.
In what order should you install components?
Install components in the case in this order: power supply, drives, motherboard, and cards.