Well congrats on getting to the endgame! As far as starter endgame builds go, this isn't bad at all- so my advice is below, please note I'm speaking from a damage perspective, but your own personal preferences come before all that.
Here is my own build- http://www.stoacademy.com/tools/skillpla...erdps_7241
The way that DPS works loosely speaking is that the more critical hits you land, and how powerful they are the more DPS you will have. the [Crtd] modifier gives you more damage per crit, and the [crtdh] value gives you more critical hit chance, although you would get this for consoles and not weapons. [Pen] modifiers give you a chance to bypass armor and so the defense value of your targets. Therefore one of the best weapons out there today are crtdx3 pens antiprotons. Antiproton weapons give you more critical severity damage which is why they are the weapon type of choice for DPS builds. Its generally not a good idea to mix weapon types, as it is better to use 1 for the tactical console boosts.
Now looking at your build personally I would get all AP beam arrays (considering that the andromeda has a very slow turn rate) and maybe just 1 torp on the front. For aft weapons you can get the kinetic cutting beam from the omega reputation which works with the assimilated module for a set bonus. (see below)
2) Set- Warp Core, Shield, Engine and Deflector
I would get a set from the reputation system instead of the ones from the missions. Currently the Iconian set is the best for raw damage boosts, however I personally like the AMACO better, for the nice visual effects and the high shield capacity among other things. The kobali set is meant to be not bad, so maybe play over the mission a couple of times to get the impulse engine as well to get the set boosts from having all 3.
Tactical- The best tactical consoles are the vulnerability locators with the +AP modifier from the fleet embassy. They boost critical hit chance, which you would want to have a value of above 20% on your ship I would use all 3 slots for them.
Science- The plasma damage weapons signature nullifiers +flow are currently the console of choice because the plasma explosion they give gives you extra damage, along with the flow boost for the plasmonic leech console. This console is regarded as one of the best in game as it replenishes power levels when firing, (you want your power levels to be high when doing damage as they boost damage, in particular 125 as much as possible on weapons). As such this console is incredibly expensive on the exchange- don't know current prices but it was once 117 million EC. Its not absolutely necessary but a great asset to have.
Engineering consoles- I would get an EPS flow regulator for power levels, and a fleet neutronium armor, from the fleet dilithium mine. From there I would also get the assimilated module, a really useful console, which will boost crtd and ctdh. To boost critical hit chance you could get the zero point energy conduit from the romulan reputation. Lastly then I would put the andromeda's console on.
Tactical- For a beam ship, Beam Fire at Will is the most important power to have. I would replace the torp HY I with BFAW I for the ensign power. Additionally replace the other THY with a Tactical team I- absolutely essential for extra damage and shield distribution.
Science- I would swap Shield transfer with Science team II, which provides shield heals along with getting rid of debuffs.
Engineering- I would only use the commander engineering slot for engineering powers and use the command specialization slot for all 3 command powers. First of all, I would swap the eject warp plasma for Directed modulation which will bypass shields. Next, I would swap reverse shield polarity with engineering team III for a large hull heal and debuff cleans. Then for your two remaining powers, I would get both Emergeny power to weapons I and II as this is needed to keep weapons power levels high, and having both will reduce the cool down on them.
Command- I don't use command ships so I'm afraid i don't really know much about command space powers- check on reddit.com
and on the forums- I have heard that some are more useful then others, but I would use the command powers here.
5) Skills- The new skill system is about to come into effect, so I would hold off on doing a respec and see what the DPS players have recommended on skills when its all been tested and recommendations come in.
Well hope this helps, welcome to STOA again, and hope to see you around in game some time.