grounded emitter or common collector circuit or something else?
With a common collector configuration the output voltage can never be larger than in the input so you will be limited to the 5V output of the Arduino (minus 0.7V for the bBE junction).

So the most appropriate is a common emitter.

You need to control the base current with the common emitter so use a resistor from the Arduino that gives about 1/10 of the collector current.  Since you have a 700mA LED that will need about 70mA base drive which is too much for the Arduino (can only supply a maximum of 20mA).

You could use a darlington connected transistor which has higher gain, for example a TIP120.  You could run that with just 1% of the collector current into the base - i.e. 7mA.  A resistor of about 470 ohm would be good.  Alternatively you could use a power MOSFET, select one with a logic level gate drive as you only have 5V from the Arduino.  A gate resistor is not necessary. The resistor in series would need to be (24 - 3.4)/0.7 = 29 ohm.  This resistor needs to dissipate ~15 Watts so it will need to be a large wire wound one or multiple resistors in series/parallel to dissipate the heat - it will get hot.

Since you have 24V to power the LEDs it is better to put the 4 LEDs in series as you have shown.   You will only need one series resistor and the total power consumption will be less as lighting all 4 LEDs will take just 350mA - if you put them in parallel they will take 1.4A.  The total voltage is about 12.8V leaving about 11V across the resistor. This resistor should then be 31 ohm (about the same as the other one).  It will only dissipate ~4Watts so doesn't need to be as large as the other.

Using 24V this circuit is not going to be efficient as most of the power is dissipated in the resistors. It would be better if it could be driven from 12V or 5V.  12V would probably not be enough to drive the 4 LEDs in series so they could be split into two groups of two.  With 5V each LED would get its own series resistor.

For a great deal of extra complexity you could increase the efficiency by driving the LEDs from a switching supplies.