Which model may be best for outcome of a surgery? New to data science and am trying to be a self-starter and implement advanced data analytics in my subspecialty of surgery. Below is a description of my data set. I know that I will have to explore multiple methods, but wanted to get your take on which you think may be best. I will most likely be using R to achieve this analysis.


Have a data set with about 200 patients (rows)
Each patient has about 10-15 variables (preoperative and intraoperative)
Each patient has undergone either nonoperative or operative management
Success in nonoperative or operative management is determined by a questionnaire that patients fill out 1 year after they are seen. This questionnaire gives a binary outcome on whether they (1) Benefited or (2) Did not Benefit from the surgery. 


My questions for the study are as follows:


In the surgery group, I am trying to find out which variables lead to patients (1) Benefit vs (2) Do not benefit from surgery, and create a model which can better help predict which patients we can operate on (I have left out some details such as patient population, type of surgery, etc).
In the second study, I would like to determine which patients we should operate on. In other words, I would like to find out which preoperative characteristics make some patients more likely to benefit from (1) Operative treatment vs (2) Nonoperative treatment and in this case the outcome will also be binary from the questionnaire.


I have tried linear and logistic regressions for this which have not been very good, hence why I am trying to learn more advanced models. 

Models which are easier to comprehend by clinicians are more valuable which is why I haven't delved into neural nets. I appreciate any and all advice that can be provided. In addition, if I expand this data set to 600 people, would you use another model? I don't have access to large servers so most of this will be done on my laptop though I can use online resources if necessary (Azure etc).

Thank you all for your help and input.
Question 1: I would propose Decision Trees as a first thing you should look into, as they are easy to implement and the results are straightforward to interpret. 
You will end up with a tree-structure, where the nodes hold intervals/values of your variables. At each node, the tree tries to split your data most efficiently into your binary classifications $C_1$ and $C_2$. Thus, in the end, you will be able to extract most important features in your variables at the top of the tree. A typical measure of "efficiency" when selecting attributes is Entropy. 

Question 2: I think it is also solved with the above method. For each node of the tree you know the amount of $C_1$ and $C_2$ classifications on the left and on the right. Assume your attribute in the node is "Has diabetes". Your data (and thus the tree) tells you, 100 out of 110 patients "failed" the operation if the person had diabetes. Thus, you can give an estimate about how certain attributed contribute to success of your operations, and conclude it would not make much sense to operate the given person. 

Nonetheless, always be careful about how you interpret the results. You should not try to interpret attributes that split small subgroups, since this can easily lead to false assumptions about real-world behaviors.