Hi Lindsay!
I would recommend getting the Park Hopper if you're looking to visit multiple Parks on the same day. The Base ticket only entitles you to 1 Theme Park per day. But tackling 4 Parks in 2 days would be a major undertaking! As a family, we generally put a day to the side for each park. Or, we get the Park Hopper, where we can jump around each day. Magic Kingdom and Epcot can take 2 days by themselves if you're hitting all the attractions, stopping to eat, catching a parade, plus taking maybe a show or two in. Hollywood Studios always seems to be our shortest visit, in part because we have a toddler and couldn't make it on some of the rides. With it being your first trip, you definitely want to have some time to soak it all in; each theme park is pretty massive...
However, 4 Parks in 2 days may be do-able only if you specifically select the rides you want to get on in each park, then study the maps beforehand, so when you get to the Park you know exactly which direction to head.
who knows? The more I think about it, it sounds like a great challenge. "Disney's Amazing Race" or something like that (smile).
Good Luck on your first trip! May it be filled with magical memories!