Wow.
Okay, as a base, let's look at rods that have each of those as at-will abilities.
For command word abilities, it's spell level x caster level x 1,800. Staves have a minimum caster level of 8th, so we can assume using that minimum gives us the "at caster's level" effect.
So the raw costs are:
Wall of Fire: 4 x 8 x 1800 = 57,600 gp
Fireball: 3 x 8 x 1800 = 43,200 gp
Burning hands: 1 x 8 x 1800 = 14,400 gp
Now, staves actually reduce the cost of abilities after the most expensive, but they all draw from the same pool of charges. Other items multiply the cost of abilities after the first by 50% since it's all in one "slot" (effectively rods take the unmentioned "hand held" slot). But, since you can only do one of these at a time, and only every x rounds, I'd actually use the base prices and call it a wash. You can use the thing slightly more than ½ of your total rounds – six out of ten rounds, which I don't think is worth a true reduction in price (YMMV), but is good enough to make secondary abilities not cost more.
Or in other words, I'd say 115,200 gp.