GLM regression - help choosing model specification

I think I need to use a Poisson-family regression or negative binomial regression. My variables are as follows: Y is an integer value ranging from 0 to ~1200. It represents sums (number of species summed over an areal unit). There are in fact many zeroes but no negative values. X1 is a categorical variable, x2 is continuous (which also contains a few zeroes) and X3 is categorical. All are positive values. Variance of Y is larger than the mean.

Y            X1         x2                X3
Min.   :   0.00   01:29551  Min.   : 0.000   2009 : 2474
1st Qu.:   5.00   02:72289  1st Qu.: 7.646   2010:28484
Median :  23.00             Median :13.000   2011:  882
Mean   :  77.21             Mean   :12.634
3rd Qu.:  80.00             3rd Qu.:17.000
Max.   :1155.00             Max.   :30.000 Y is negatively skewed (i.e., skewed to the left). Histograms of residuals from a basic linear model (lm) and a QQ plot indicates the results are also skewed. The residuals plotted against fitted values also indicate that a linear model may not be appropriate because more points are above the line than below (across all values of x). Is it correct to use GLM with a poisson distribution with log link in this case?

Mydata.poisson  <- glm(Y~X1 +x2 + X3 +x2:X3, family=poisson, data=mydata)

Or more specifically, should I use the quasi-poisson? (in the regular poisson, my df was “31839 Total (i.e. Null); 31833 Residual”, Null Deviance was 1085000 and Residual deviance was 1079000). Also I believe this would be a case where I need to use a zero-inflated model? I am confused as to how to set this kind of model up. I read that a negative binomial distribution is similar to a poisson distribution, and better to use when the variance of your Y is greater than its mean, but isn't a binomial regression used when your response is binary?

EDIT: I have used the following negative binomial model:

Mydata.nb  <- glm.nb(Y~X1 +x2 + X3 +x2:X3, data=mydata)

I understand that one should still check the residuals to see if the assumption of linearity holds (e.g., see discussion here: What are the assumptions of negative binomial regression?). A plot of the standardized residuals is included below and suggests that perhaps the relationship is not very linear. Would you agree? How can I resolve this? • Your response is not binary, it's from 0 to 1200. – James Sep 2 '14 at 18:51
• Yes that is exactly my point. I was wondering if there was a way to do negative binomial regression with a non-binary response. I guess not. – sth Sep 2 '14 at 19:26
• Negative Binomial takes count data, just like Poisson. Binomial (logistic) takes {0, 1} response. – James Sep 2 '14 at 19:48
• oh! You're right. I didn't understand that. Thank you. – sth Sep 2 '14 at 19:59
• I'd like to see a plot of unstandardized residuals versus observed $y$ values, if it's at all readable. Also, what are you actually modeling here? Substantive understanding always helps. – shadowtalker Oct 8 '14 at 5:56