For your first time, I would stay away from major holidays (Easter, Christmas, etc.). As far as being able to see all the shows and things, Summer is probably best, though it can be quite crowded. I would guess that either early or late summer would be better, when some schools might be in, but that question might be better answered by a CA resident who frequents DL. In summer, there are more shows, fireworks, etc., and the park hours are longer, but there are more lines. In off-peak season, there are fewer lines, but some attractions may be closed for refurbishment and there are fewer shows.
If you go during the summer, my guess is that weekdays would be slightly better than weekends.
I would allow a minimum of 3-4 days to experience everything in DL. I was there last October (relatively slow season), we stayed there for 4 days and we were able to cover everything in a very leisurely manner (taking breaks, having sit-down lunches, etc.).
Also, since you're coming from VA and if you don't think you'll make it back to CA in a while, you might want to consider doing things like Universal Studios (pretty different from Orlando's), Knott's Berry Farm, and if you have time, a couple days in San Diego to go to Sea World and the Zoo.