You can count on working every other weekend-some places have Fri and Sat nights as the nightshift weekend. Rarely, will you be scheduled 3 on and 4 off. It might even be one on-one off- one on and so forth. Whatever the unit's needs are is where you will be plugged in.
You would have to talk to your nurse manager regarding a set schedule. I'm sure there are some that wouldn't mind to have someone work every Fri-Sun. Weekends are typically the hardest shifts to fill. I know I hated having to work every other. But a Mon-Wed set schedule would be a schedule someone with more seniority would have a better chance of getting than someone just starting out. Good luck.