Best mosfet for switching DC from 5v Arduino pin.

mwhens:
I want to learn, but it all seems so complicated to me, mostly all the graphs.
But I try to understand.

You use the STP40NF10L. That would be a better option you say.
When I compare them I see it has a higher voltage and amp rating, that I can understand.
It has also other differences I can't understand...

The STP40NF10L has Rds(on) max "33 mOhm @ 20A, 10V" The IRLZ34NPBF has "35 mOhm @ 16A, 10V"
I don't understand this, your talking about 0.036 ohm max at Vgs=5v and Id=20A.
What does this digikey spec tells me, and wich would be better, lower Ohm's?

Yes lower Ron is better, but very little differenc .033 ohms Vs .035 ohms, and your using it at 4 amps load, so no reason to pick one over the other just on this specification alone.

There are more differences...
The STP40NF10L has "Vgs(th) (Max) @ Id" = "2.5V @ 250µA"
The IRLZ34NPBF has "2V @ 250µA"
Vgs should be as low as posible I believe?
The STP40NF10L has "2.5V @ 250µA" the IRLZ34NPBF has "2V @ 250µA"
The STP40NF10L has a higher Vgs? That means thats a plus for the IRLZ34NPBF?

No, all should be looked at at what the Ron and current flow allowed with 4.5 to 5vdc on the gate. These threshold values all fall in the 'logic level mosfet' catagory, again no deal breaker or maker here.

Another spec,
Gate Charge (Qg) @ Vgs, STP40NF10L has "64nC @ 5V" the IRLZ34NPBF has "25nC @ 5V
"
Does that mean the IRLZ34NPBF need less than half the power to switch than the STP40NF10L?
Thats another plus for the IRLZ34NPBF?
Another spec...
Input Capacitance (Ciss) @ Vds, The STP40NF10L has "2300pF @ 25V", the IRLZ34NPBF has "880pF @ 25V
". The STP40NF10L has much more with it's 2300pF. Does that mean how much power is needed to switch on? The IRLZ34NPBF is the better one here?

Both those spec give an indication of how much charging and discharging current the arduino output pin has to supply to make the mosfet switch from on to off and off to on. Lower capacitance is better in this case and I would make it the deciding factor if all other specs meet the application.

Again I'm concerned about that small transistor you show in your picture. One usually tries to drive a power mosfet directly from the arduino output pin to the gate of the mosfet. Arduino ground must be wired to the external power supply negative terminal. Lastly it's a good idea to wire a 10k ohm resistor directly from the gate to source terminal on the mosfet. This will insure the mosfet turns off if you happen to turn off power to the arduino, but external power for the mosfet load is still on.