What is the best vegetable oil for this recipe? I 'm not an experienced deep fryer and want to do it right, because I imagine these are very good.

My suggestion would be peanut oil or corn oil. The thing to keep in mind is that it needs to be an oil with a high smoke point. I would take it a little higher than Monita to 375F. Use a candy thermometer, they're cheap.

Here's a helpful Food52 column on the best oil for frying:
http://food52.com/blog/8570-what-s-the-best-oil-for-frying

I'm not sure as I didn't develop the recipe but generally speaking any vegetable oil will be ok. The real key is keeping the oil at an even temperature. This recipe doesn't given a temperature for frying but if you have a thermometer that can go in oil then use it to keep the oil at around 365 degreesF. If you don't have one then watch your fries so that they don;t brown on the outside too quickly. Keep adjusting your flame so that the fries cook evenly

Monita, please what kind of vegetable oil was used for the photo of the perfect looking chick pea fries?

A vegetable oil is best