Well, you don't necessarily need classical theory in order to play sufficiently to have fun. I know all my theory, but it really is not essential to play for fun. Just learn chord theory and scales (circle of 5ths make this much easier). Once you know how to play all the different chords and scales, learn different chord progressions and create your melodies out of the scales you've learned. You don't necessarily need to know what finger goes on the B, which finger goes on the D#, and what finger goes on the F#, just where the next note is from your root (in this case the B) and the next note above that. Here's some examples that show you HOW to create the chord instead of telling you WHAT the chord is:
Major chord: You start with your root (this is the note that you will build your chord from). We'll pick C natural. From your root the major third is 5 keys above it (including the root). So C, C#/Db, D, D#/Eb, E. E is your third. Then the fifth (which will complete your major chord) is a minor third above that. A minor third is 4 keys as opposed to 5. E, F, F#/Gb, G. G is your fifth, therefore your C Major chord consists of C, E and G. Now apply this to any other root and you can play any major chord (I.E. root=F means third=A and fifth=C).
Minor Chord: Start with a root (we'll use C again for consistency). It is almost the same procedure as a major chord, but reversed. As in, the third is only four half steps above the root (C, C#/Db, D, D#/Eb) and the fifth is five half steps above that (Eb, F, F#/Gb, G).
The root and the fifth will always be the same between a major and minor chord. What makes the difference is the third which you play a half step lower in a minor chord. C E G becomes C Eb G.
Now, once you learn your scales, you can play just about anything. A major scale also starts with a root (once again we will use C). From the root the progression goes: whole step, whole step, half step, whole, whole, whole, half. So C, D, E, F, G, A, B, C. As practice, take any random note an apply the same formula. It will be tough at first, but it will get into your fingers eventually.
A minor scale is a little more tricky. There are three types of minor scales: Natural, Harmonic, and Melodic. A minor scale is relative to another major scale. The root of the scale begins on the sixth scale degree of its relative major scale. The relative minor scale to C Major (the scale we just discussed) would be A. From here the natural minor progression proceeds as follows: Whole, half, whole, whole, half, whole, whole or A, B, C, D, E, F, G, A. A natural minor scales means exact that, it is natural. No modifications. A harmonic minor scale is slightly different. It is basically the same except you sharp the seventh note in the scale, the G. So a harmonic minor scale is whole, half, whole, whole, half, whole + half (minor third), half or A, B, C, D, E, F, G#, A. And the final minor scale, the melodic minor, is the trickiest. In this scale, the sixth and seventh degree are sharped as you ascend the scale, but not as you descend. So in A, the scale is A, B, C, D, E, F#, G#, A on the way up and A, B, C, D, E, F, G, A on the way down.
That is a good stepping stone for setting you on the right path to basic playing. Once you have a firm grasp on all that, there is little else that you must learn to achieve a sufficient level of playing. All that is left is chord progressions, pentatonic scales, some more chord theory and basic rhythm techniques and you will be able to play nearly any song well enough to keep you entertained forever.
EDIT: Certain notes are labeled as both a sharped note and a flat note. These are called Enharmonics. This means that they are the same not, but the name changes depending on what key you are in. D# is actually Eb when you are in C minor but is D# when you are in F#. The Circle of Fifths will also help you greatly when learning how different keys work.