For a recent undergraduate student in Engineering, is it better to gain some work experience (through internships/junior positions) and then go for the master when it's time or apply for a MS right away?

The best of both worlds would be to take a job and then start taking classes that will count toward your Master's degree. There is a huge opportunity cost associated with quitting your job (or not taking a job offer) and going back to school, but taking classes while you continue to earn a salary can give you a very good return on your investment--particularly if your employer has some type of tuition reimbursement program. You'll often get better value from your classes when you are working a real job at the same time. It is easier to remember theory when you have opportunities to use it to solve real problems you are facing at work. A constant supply of real world problems means you'll be able to ask deeper questions than you might think to ask if you are only taking classes. Taking classes while working full time may mean you finish in 4 or 5 years instead of 2. But even assuming no tuition reimbursement, that means you've made $160,000 during those 4 years instead of having lost $80,000 in wages in two years. If you had a guaranteed job at $80,000 per year upon graduation, it might work out to be equal in terms of money. But the reality is that you'll be on the job market as a Master's degree graduate with no real work experience vs. being a Master's degree graduate with 4 years of work experience. In other words, working a real job and taking classes that will usually help you at the increase the amount of real world success while minimizing the amount of time it takes to get there.

This is a very subjective issue because "success" is going to be evaluated differently for everyone. Doing an internship before a Masters may not make a quantifiable difference in the long run, however it may confer some advantages. Actual work experience is always valuable. You may learn something that allows you to focus your Masters work on an area that will affect your career later on. Perhaps you will discover that you want to change the direction of your studies. Perhaps you will decide to pursue something more practical than you originally had in mind or perhaps the work experience will suggest a direction you hadn't previously considered. In any case, once you have your graduate degree and begin looking for work, previous work experience can only help you and make you more attractive to a prospective employer than someone with only academic credentials.  It's hard to see a downside to getting some real-world experience at this point. It won't guarantee increased career success, but how could it hurt?