Somewhere out there in an alternative time line to our own, exists the Time Lords. During the years just before the war with the Enemy in the 8th doctor BBC novels, the Time Lords already are aware that in the future they will fight a time active enemy (because present day time lords cross time lines with future ones, which isn't supposed to happen). They have been building weapons and scanning future time lines looking for signs of this enemy.
Then one day they discover this abomination. Shocked that human imagination with Time Lord knowledge leads to so much wank they decide to find a human, connect them up to the Matrix and imbue them with Time Lord knowledge, and give them time lord physiology to match. Lets face it, Donna wasn't the sharpest tool in the shed to they decide to pick someone smarter. They pick YOU. So now armed with whatever Time Lord knowledge available to DW readers, you are also aware of whatever 8 th doctor adventures have happened up to that point as the TL keep track of their errant citizen.
Your task is to design new devices, preferably weapons for them to fight anyone. There is no rebelling because they programmed you so you can't. They however are generous as they will
a) give you a type 40 TARDIS to go where you want after the Enemy has been defeated
b) give you as many regenerations as you want should you want it
c) Let you even use block transfer computations to create your own companions should you want them
These are incentives for you to do a good job. If you can't they wipe your memory and return you to your place of origin.
The rules are
a) you must build something from known TL tech or alien technology the TL have on hand (see below). So you can't do what Donna did and make whatever device that the plot dictates it needs. The human advantage is supposed to lie in designing things the TL won't think of rather than discovering new scientific breakthroughs
b) no I am going to scan for future tech and incorporate that - so the ST Henry Starling tactic isn't allowed
c) try and have it within known TL industrial capacities, so you can't build a giant galaxy size ship called the "compensating for something"
d) No I am going to incorporate wank whoverse race of the week alien tech unless the Time Lords have said technology on hand. So saying you want to use some weapon from the Deathsmiths of Goth is out, however Raston warrior robot is in since there is at least one in the death zone.
e) try to be a bit more innovative than just I will build a bigger war TARDIS with x times as many weapons etc.
f) lists the sources (if you know them) which capabilities you will mix and match
g) try and justify why this invention would be useful rather than just because it looks cool.
Some sources which might help you
discontinuity guide
Doctor who wikia
My contributions would be
a) from my own fan fiction idea a weapons platforms which is essentially a giant planet, kept in similar defenses to Gallifrey. Think of this as the TL equivalent of the SW galaxy gun (although it can have tactical as well as strategic implications) where the time active enemy most probably has the ability to defend itself against Time scoops and time loops. Its missiles are essentially small TARDISes with at least equivalent range as a type 40. Each missile's dimension on the outside will be much smaller than a TARDIS (harder to detect and hence intercept) and the inside contains various bombs such as singularity bombs (Lungbarrow) etc. The missiles can be programmed to time ram opposing ships the same way the Doctor could time ram the Master's TARDIS (The time monster).
Now you might say why don't we just turn Gallifrey into this weapons platforms. Well the advantage is the weapons platform only has to be a weapon so you can build several of them. They can also be hidden whereas Gallifrey's location is known. By having a planet size platform you increase the surface area allowing them to fire lots and lots of missiles at once for example is the enemy ships has just been detected.
Keep in mind that the Doctor's TARDIS could reach close to the big bang (Castrovavla, Timeless) and the year 100 trillion (utopia). In spaceit could reach the "edge" of the universe (Planet of evil) with the universe estimated at 93 billion LY in diameter. Given this I am pretty sure the missiles would pretty much cover most of where the war would be fought.
b) unlimited energy source, ok maybe
This smacks like a magic the gathering infinite combo, but because of what the DW writers have established over the years I am surprise somewhat didn't think to use this "cheat" long ago.
Basically in the normal universe Energy = Mass x speed of light squared. Its established in the vortex Energy = Mass x speed of light cubed (the time monster). In other words physics are different in different dimensions in the Whoverse. Even funkier in the higher dimensions (where the TL have limited knowledge) Energy = mass x speed of light to the fourth power (quantum archangel). Don't look at me, I don't write this stuff.

Now the TARDIS has a matter converter (Castrovavla) which converts rooms in the TARDIS to energy for that extra boost. We know TARDISes can enter the vortex and that several engagements in the Dalek fleet took place in the vortex. Now put your hands those that can see where this is going. Simply bring matter with a TARDIS into the vortex, convert it into energy, then bring the energy back to N- space and convert into much more matter, then bring it back into the vortex and repeat. Obviously you lose a bit of energy in the conversion process from thermodynamics, but it shouldn't offset the extra energy you gained close to c times. The possible barrier is in how much energy does it take to enter the vortex and exiting the vortex.
The limiting step is how much energy TARDISes can hold, but I am going to say a lot since war TARDISes were supposed to be able to drain stars dry and the Doctor himself used energy from a supernovae to communicate with Rose through the dimensional barrier (Doomsday).
Now I don't think this excess energy necessarily translates into much stronger shields or powerful weapons, but with it the Time Lords could theoretically build more weapons from this excess energy since they can convert it into matter.