Weapon layout is probably easiest to cover, as a science vessel goes it will have three (3) fore and three (3) aft weapon slots (Unless in the sixth tier Cryptic gives us more)
Second Torpedo or Second Beam weapon or Mine layer
Torpedo or Mine Layer (depending on play style)
Turret or second beam weapon
How you set up your weapons depends on your play style, are you going to fly in close and mix it up or circle the battle buffing and healing allies and occasionally firing into the fray ?
Science vessels can only utilize turrets, they cannot mount cannons, it is also good to have a mix of weapons rather than just all one type. What type of weapon you use is up to you there's phaser, plasma, disrupter each having their own color and damage rating. If your using turrets you can set them to auto-fire and they keep firing as long as their is a target. They don't do massive amounts of damage but is is consistent damage.
As far as skills and tactics you may want to read up on what type of abilities your Bridge Officers and ship Captain will get. For me I like using Jam Sensors and Tractor Beam. After you've read what you will be able to do someone will be able to help you contour where to spend you points and focus on the skills you like
I can't comment on end game stuff but as of right now I've been focusing more on having:
I find as of now this works the best for me, allowing me to not worry as much about arcs and still able to fire on a majority of targets (also gives me 2 guns when fleeing or trying to stay infront of a target). I prefer the photon torps for their higher dps.
I found mines to be a nusiance as they would often hit things I didn't want them to and having explosions take them out.
As of now I like the disruptors because the seem to hit hull harder.
As for powers, I've been running both science and engineering team I, and transfer shields I. (The ideal to me being transfer shields II and science team III down the road. Photonic officer sounds like it can be good, but I don't have it yet.
Tykens rift seems like it could be good, and if not it looks cool enough for me to keep using it. Not sure about tachyon beam at full power.
Id suggest planning on using a few types of officers, ones that heal, ones to debuff as well so you can swap as needed