I just wanna play with and do some testing on various VCC / VEE levels.
1. Less than 1 watt needed on output / think "LINE LEVEL"
Not sure why you want to test with various levels for VCC and VEE unless you are also playing around with the load resistance while maintaining your 1 W specification. In general, you need a peak voltage into the load (assuming a speaker) that is sqrt(2*power*load). So if this were 8 Ohms and 1 W, then 4V peak. If it's not bridged (and I'm assuming its not) then you would need 8 V peak to peak. And that implies about another 2-4 V added. So a +12 V and ground or else +/- 6 V would be enough. Not much need to play with those values. Using larger voltages would be wasteful and using less would remove headroom you may need.
2. Push /Pull
3. Class AB(?) Can number 4 happen with Class A?
4. Bi Polar supply
Output stages driving speakers at 1 W are always push-pull (2-quadrant.) Attempting to use a passive resistor for one of the quadrants is... not advised.
Bipolar supplies can be used with class-A and with class-AB. The circuits don't care. But class-A is very very inefficient as a power stage. (It's just fine as a voltage gain stage, though.) So you probably want a class-AB output stage with a class-A voltage gain stage. Negative feedback will also be a necessity, I think, for good THD as well as setting the gain and/or volume.
5. discrete
That can be done. In the class-AB case, you may need to include provisions for setting the quiescent current using a VBE-multiplier with a potentiometer (or some other means.) For relatively simpler designs, anyway. (Transistors vary quite a bit, one to another. And so does the operating temperature. So you may need to play around a bit to get it set.)
What else do I need to spec? It almost seems like more of a preamp?
You mentioned "line level". That's almost a spec. (The meaning varies a little bit based on application domain. But close enough for horse shoes.)
If you intend on using electrets, you may need a pre-amp stage. But I think you are just saying "line level" so I'd guess you can avoid any specialized pre-amp stage and go straight to a nice class-A voltage amplifier stage followed by a class-AB power stage and some NFB (negative feedback.) 1 W isn't too hard, though it's not entirely trivial either. It's a good target for learning.
Line level is around 700 mV rms, I think (I'm no expert on it.) And an 8 Ohm speaker at 1 W would need about 2.9 V rms. So the voltage gain is only 4, if my math isn't failing me. That's actually pretty easy to achieve. So a lot of negative feedback can be used to correct many errors (thermal drift and so on) while also achieving the desired voltage gain, without stretching things. The complexity will be more at the class-AB end. Though even here the 1 W spec means a lot of otherwise difficult problems (dissipation, for example) are far less problematic.