The 10k is simply to limit the amount of current from the GPIO pin through the transistor. Without a resistor the GPIO pin would see an almost short to gnd, leading to the Pi getting toasted (should have a certain degree of protection I would think) or the transistor gettign cooked (due to the limited amount of current, I;d expect the Pi to die first). Anything in the 1k-10k range should work fine.

The other 2 resistors are being used as a voltage divider to reduce the 7.2V to aprox 4V. One thing to note is the 310R will basically be connected direct to ground when the transistor is switched on, so you want to ensure it's got a high enough power rating.
So current is 7.2V/310R = 23mA, then Power is 7.2V*0.023A=0.16W. An 1/8W resistor is only 0.125W, so you may want a 1/4W resistor for durability, or two 1/8w in series or parallel, if you can't guarantee long periods of being the transistor being switched on.

Just done a quick search, and 1/4W are actually cheaper. I've been doing too much with SMD lately where 1/8W is normal!

10k - RS own brand 1/4W- 707-7745 12p for 10
390R -RS 1/4W - 707-7634 16p for 10
309R (nearest to 310R) - either Vishay 3/5 (0.6)W - 683-3500 -1.25 for 25 OR TE 1/4W - 754-9072 1.07 for 5
The TE have a tighter tolerance (0.1% v 1%)