Does it look like the "Spider" variety?

It seems to be nothing more than the 'Typical' variety, which isn't a bad thing by any means! Once it adjusts to your conditions and gets colored up a bit more it might be easier to stick a label on it.

nice plant. it is indeed a typical variety.
you are quite lucky to have such wonderful plant. flytraps usually send their leaves upwards into the air as temperatures rise and days become warmer & longer. this is natural for them to react such ways. patience is require in order for them to perk up.

I didn't get anything in that first picture to show its size. That is a 4 INCH cube... not one of those little cubes. Could it be a larger variety of typical or a SW Giant?

Sure looks like a 'Typical'. But it's a very nice looking typical! If kept outside, its trap inside should become more pink.