I’m a structural engineer. I feel that a master’s degree is very helpful but it’s not mandatory. I had several classes in grad school that were really excellent. You go more into the “why” of design instead of just “how.”
I would recommend top state schools for a master’s degree. Their research facilities are amazing. I went to UT Austin. Several of my professors were in the National Academy of Engineering. Their lab is one of the largest in the world.
Just see how you feel when you’re a senior. Talk to your professors and see what they recommend. Another possibility would be to work for a couple of years and then go back for your MS. I was fully funded and my stipend was enough to cover my living expenses.