Re: "No security teams on the bridge. We must've been taken by surpris
Since Tactical and Security are a combo post
They were separate posts in TNG until Tasha got gobbled up, after which they had Worf do double-duty rather than introducing a new character. As for TOS, well, they seemed to make Chekov the tactical/security officer in the movies, but he was navigator in the series. Memory Alpha has this humorous nugget:
Although he mainly served as the Navigator aboard the USS Enterprise NCC 1701/A, he has had the most variable amount of positions than any other senior crewmember under Captain James T. Kirk.
I actually don't mind this, because, as with modern-day astronauts, virtually every crew member needs to be multi-skilled, so they can cover someone else's role if required in times of duress. In any case, plotting navigational routes is only going to take up a small amount of an officer's time, because most time will pass while they're underway, in which case it's downright sensible to put that officer to good use with whatever's handy and doesn't interfere with his or her other responsibilities.
Now... as for the 'security teams' issue...
Starfleet is a military organization. EVERY crew member should be subjected to 'basic training', just as is every enlisted military officer in today's military. This would include training in use of a firearm, when it's okay to use it, basic tactics, etc, etc. Every crew member aboard a starship is a scientist, historian, navigator, MP, etc, and they're ALSO soldiers who may be given the order to fight at a moment's notice. Instead of calling for security and then standing there defenseless until said security shows up, they should all be armed (or have arms nearby) and be ready to mobilize at any time, and 'calling for security' should be tantamount to calling for
backup.