Suppose there are 3 advertisers who want to show an ad on a site. If a user clicks on an ad and makes a purchase the host of the site makes a certain percentage of the purchase. Suppose we have historical data on all 3 ads for a set of individuals, and we have variables: 


conversion(0/1: the user clicked on the ad and made a purchase)    
gender(male/female)
the amount of time since the last visit, etc. 


The owner of the site wants to know what ad to show to a particular person with a given set of characteristics(variables in historical data). What would be a good model for this? 

It seems that there is no "single" response variable. I was thinking of building a logistic regression where conversion(0/1) is dependent variable, and type of ad(3 values) is independent variable but I am not sure if this is correct. Do you have any suggestions on what a good modeling paradigm would be?

With:
$$
x' = \frac{x - \min{x}}{\max{x} - \min{x}}
$$
you normalize your feature $x$ in $[0,1]$.
To normalize in $[-1,1]$ you can use:
$$
x'' = 2\frac{x - \min{x}}{\max{x} - \min{x}} - 1
$$
In general, you can always get a new variable $x'''$ in $[a,b]$:
$$
x''' = (b-a)\frac{x - \min{x}}{\max{x} - \min{x}} + a
$$
And in case you want to bring a variable back to its original value you can do it because these are linear transformations and thus invertible. For example:
$$
x = (x''' - a)\frac{(\max{x} - \min{x})}{b-a} + \min{x}
$$
An example in Python:
import numpy as np
x = np.array([1, 3, 4, 5, -1, -7])
# goal : range [0, 1]
x1 = (x - min(x)) / ( max(x) - min(x) )
print(x1)
>>> [0.66666667 0.83333333 0.91666667 1. 0.5 0.]

