I have data sample size of almost 15,000 cases. The dependent variable is a dichotomous variable stating whether the patient has the disease or not, Yes=1, and No=0. I have 12 more independent variables which are continuous as well as dichotomous. My question here is, before I apply the logistic regression, I need to know which parameters have a great impact on the DV; how do I do that? Secondly, there are 7 different methods of using binary logistic regression like enter, forward conditional, forward LR, etc; what is the basic difference between these? I couldn't find any matter on this on the internet.
The methods of "doing the regression" that you refer to (with SPSS terminology) are really methods of variable selection. You shouldn't do any kind of automatic variable selection. You should just use all your candidate variables in the model, and let them stay there. Using data for variable selection
does have a very poor track record of actually finding the correct variables,
invalidates posterior inference. Very thorough discussion.
The regression model is what tells you which variables are important and which not. For logistic regression it is often advised that with the effective number of observations $N$ (number of obs in the minority class), $N$ should be at least 15 times the number of parameters. More details here. With 15000 observations that should not be a problem for you, even with only 10% in the minority class. With 1% in the minority class you could have problems. Just fit the full model and validate it!
You say you have some non-linearities. That can be solved by representing variables who acts nonlinearly with splines. For instance, I would always represent
age via splines. See also the useful information in the comments.