Well you might not be running an escort but your science ship's weapons will still improve and since you have rather few of them... that might be a good idea... you can either super specialize in what your ship is already good at or you can spend some points bringing up the spots in where it lacks... that comes down to play style though. There's no reason why you're olympic class hospital ship shouldn't be able to hold it's own... but if you want that extra punch for when the going get's tough and even buffs/debuffs aren't helping... invest some in the tactical stuff... Keep in mind also that BOff skills can help augment your abilities as well! It's very confusing without a skills tree for sure.
And don't tell the ingame skills window IS a tree. Training in Science Team Leader does not open up Escort vessels as it shows in my window. The skills are not listed by order of which they unlock each other.
So I would like to be a medic, and I see that there is a medic skill. But I don't want to be ineffective in space. I'm not sure if everyone really should be upgrading weapons, because let's face it, we all need them. But I'm not going to be in an escort vessel.
There really is no "ineffective" in space or on the ground. You put points into what you want and play your character as you want. No matter how many points you put into Starship Energy Weapons, you'll never be as good with them as someone who flys an escort. That's just the way it works, so don't worry about it. There are more than enough people playing STO so that if you join a team, someone there will complement your strengths and cover for your weaknesses.
Besides, they cover this in one of the FAQs they have about STO. You have the ability to go as specific or generic as you'd like your char to be and it won't be game-breaking.
But, and I cannot stress this enough, go hunting through the game and READ. Open your powers menu (P by default). There it will give you details descriptions for your powers and what skills modify them. Then you can choose what skills you want to put points into.
Even then, most skills give innate bonuses to everyday things you do in game, so there is no right or wrong answer.