Comparing two quasipoisson glm models 
Have these results but not sure how to interpret them to pick the best fitting model, I think the high p value suggests I should go with model 1? Also in terms of the order that I put the models in, which model is nested?
 A: It depends on what sort of comparison you make. In terms of AIC a p-value of 0.15 can mean that both models are equivalent (if the difference in number of parameters is only 1). Or 0.11 (if the difference in number of parameters is 3)
Why can't we use AIC and p-value variable selection within the same model building exercise?
Quasipoisson has no likelihood function, which is necessary for computation of AIC and likelihoodratios (but there is I believe still something like quasiAIC). Anyways, in a model comparison where the p-value is around 0.15 (for one degree of freedom change) or around 0.11 (for three degrees of freedom change) the AIC difference of the two models will be small, so for quasipoisson one might consider a p-value of 0.15 as not such a large p-value that both models are very much unequal.

Also in terms of the order that I put the models in, which model is nested?

This F-test is always expressing the change in the residuals/deviance when you make the change to the model with more parameters (independent from the order of the models, although what will change is that the deviance and degrees of freedom are either positive or negative). When the F-score is large then a significant change (if you look at p-value) or information change (when you compare AIC) has been made by adding more parameters.
