Here are some ideas for playing a minor 12-bar blues. In its most basic form a 12-bar blues in Am would go like this:

Am7 (4bars)    Dm7 (2 Bars)    Am7 (2bars)   Em7   Dm7    Am7    E7

Since we can use an open A,D,E string in this key we can use pedal tones. This is where the bass note stays constant, but the harmony or chord sequence moves around - leading to greater interest and harmonic complexity. You'll find a similar concept in many songs - Scarboro Fair is one, shamelessly stolen, one.

You could improvise with Am pentatonic scale, or Am blues scale, and try playing octaves too - a technique used by Wes Montgomery, Jimi Hendrix, and most other great improvisers since.

This blues can be as hard or as easy as you like - you can spice up the rhythm by playing with your thumb on the bass note, and picking the other notes of the chord slightly later.

Octaves are easier if you damp the middle string with your first finger.

Creative playing - one thing that really works is to take a chord shape you know, like E or Am7 and move it up the neck at random. You'll find some great new sounds this way, because often the addition of open strings to a chord will really bring it a new depth and make it sound more interesting - a bit of dissonance is good.

If you want to really study the chord possibilities on guitar, try Ted Greene books such as Modern Chord Progressions or Chord Chemistry, two veritable bibles for the aspiring guitarist. Ted was a great player and teacher, look him up on youtube.