It really is a supply and demand thing. I will often come home on a Saturday/Sunday but will try to leave for vacation on Mondays to at least save on that leg. Sometimes that doesn't work out as well as people travelling for business may want Monday flights.
Also if it is Jersey Week, you may not save on a Wed. flight for example as some families make a long weekend of it, rather than take the whole week. The best thing to do is to check some historic prices and decide a budget. As others said you then watch and play around (if not sign up for one of those alerts). Other than miles I feel like there really aren't as many deals as there were years ago (and some airlines are incredibly inflexible, we found they were only offering us connecting flights a few times, nonstop was not eligible).
Another tip is make sure you know what fees go with what airline. Some have higher luggage fees and charge for everything on board. I just booked Jetblue not only for the price but as it was only $15 for the checked bag (vs the other airline $25), you get free snacks/drinks onboard, and they have decent entertainment for free.
You mentioned Jersey week, are you in NJ or just going that week? I'm in NJ and we airport shop. Before we were married my husband and I had booked trips flying out of JFK or LGA (he was in Queens) and flying home to EWR (I'm in Hudson county). Likewise I went to Vegas with a friend who lives further south so I parked my car at her place for the week and her husband drove us to Philly as it saved us over $200 RT for some reason. For FL I also don't mind Spirit out of AC, but I do that when I am with family or friends that live further south, I would not drive all the way there from Hudson county myself. As I'm a 15 min cab ride from EWR for our most recent trip we didn't airport shop as the flights were low enough that parking or transport would outweigh savings.