Quant question / choosing an option strike price

Suppose I'm looking at an options chain on my screen and I've decided whether or not I want a put or a call, but I haven't decided what strike is best.  Additionally, I have a price target in my head and for whatever reason I think the stock will be priced at X on or before day Y.  I want to decide which strike will give me the largest return if I'm right, but I also want to minimize my loss in case I'm wrong.  

Is there a mathematical model for this?  Obviously Black Scholes is involved but there are too many variables that it's difficult to visualize.  And I also know zilch about quantitative finance (although I do have a degree in math so if someone points me in the right direction I should be good).  I can sit there and punch in 800 different scenarios into a calculator but obviously with a rapidly changing price you don't always have time for this.  

One thing that might be helpful is if there was a tool that would let you specify all but 1 (or 2) variable(s) of Black Scholes and then show you a 2D (or 3D) graph of the function as your variable varies.  For example, let's say I want to see what happens if I keep # of days to expiration and market price the same, but vary strike price.  It should show some kind of 2D graph that might help me make a decision if I feel confident that the price will be X at some point on a certain day (maybe I feel like an equity is going to test some key support point, for example).  Or perhaps I want to see what happens if I vary both market value and # of days to expiration but leave strike the same.  This might help me decide what would happen with a given option if I'm wrong and I let it ride too long, for example.

It seems like somewhere in here there's a numerical integration waiting to happen that I could supply a list of "probabilities" that I think represent how likely the underlying is to reach certain prices on different days during the contract period, and it would just spit out an "expected profit value" for each strike price making it a trivial decision which strike to choose.  

Am I making sense here?  Is there any kind of tool that helps with this?  Is there a more practical approach to choosing the best strike price to get in on something at?  (Even if there is a more practical approach, I'm still curious if anyone can enlighten me about a theoretical approach).

The calculator looks useful, but it seems to have some unfortunate limitations.  For one thing it only appears to support quarterly calls, unless I'm just missing something.  For example type in SPY 120 puts and it says the Bid/Ask is $5.28 / $5.56 which corresponds to the current Bid/Ask of the options expiring at the end of the month.

So that kind of diminishes the usefulness, although it does look pretty good if I'm playing with quarterly options.  

Also, the mathematician in me really wants to see an algorithm/formula for computing just a straight up "expected profit factor" given a bunch of inputs about how likely I think the price is to touch certain values on or by certain days during the contract period. In other words, an indicator that takes all the subjectivity / emotion out of the decision.  Sure, I can look at a table like this and decide on my risk/reward tolerance but it's not that easy to process an entire table of numbers like that and come to a reasonable decision in a fast paced environment.  

In theory it seems like you could just perform a double integral over the rows and columns of that table (preferably over the actual black-scholes though since it's continuous), weighting each price by some kind of "likelihood function" or probability distribution that is itself a function of time and then it would just spit out the exact strike price that gives the highest expected return.  So I'd still be interested if anyone has suggestions for references that talk about this kind of thing.