Now it's time to get your Mothership fully kitted-out for war.
Protecting the Crew Transports
When you arrive you'll be in trouble from the start; Bishop One and Bishop Two will already be under attack from Vaygr forces. You should have at least three Interceptor squadrons; send all three to whichever transport is in the most trouble, and have them attack all the Bombers there and move on. Do as Fleet Intelligence says and construct more Resource Harvesters, but not before constructing another Bomber squadron or two. Take all your Bomber squadrons you do have to the Vaygr Carrier and begin attacking its Fighter Facility. It will begin launching reinforcements the moment you approach it or have begun wearing down the Bombers attacking the transports. Once the Fighter Facility is down though, it's pretty much useless, and you can move your Bombers on to help protect the transports. If you have at least three squadrons of Bombers, that will be good enough to take down the Carrier's Fighter Facility before they all get destroyed.
With the Carrier now useless, this battle becomes a lot easier. Start creating two or three more Interceptor squadrons and send them out to Bishop Five and Bishop Six to deal with the Bombers. Ignore the Assault Craft, as they do very little damage to the transports, and will begin attacking your Interceptors when they get there.
The first transport to dock will allow you to construct a Corvette Facility, which is what you need to build Gunships. Gunships are anti-Fighter vessels, so in this case they useful. However, don't build any more than one as you will be strapped for RUs otherwise, and that won't do. Send your Gunship squadron to whatever transport is in the most trouble and have it begin attacking the Bombers there, or if you already have Interceptors, have it attack the Assault Craft trying to destroy them. Once your Gunship squadron is complete, you will be able to begin constructing Pulsar Gunships, but don't do so.
The second transport to dock will enable research; as it stands your Fighters will only get speed upgrades but you can get armour and speed upgrades for your Gunships and the Mothership, too. Don't construct any research yet, however.
At this point the Vaygr forces should be nearly gone, prompting them to Hyperspace in reinforcements in the form of anti-Fighter Frigates! However, you don't need to deal with these, as Captain Soban from the Hiigaran Defence Fleet will warp in with some Frigates of his own. These will crush the Vaygr in no time at all so keep an Interceptor there to clear up the last of the Vaygr Bombers and Assault Craft, and move the rest on to any other transport that's under attack. If there isn't one, send them close to the Vaygr Carrier, but not close enough to be shot at or to engage it; you'll see why in a moment.
The third and fourth crew transports to dock will confer sensor operations teams and powerplant teams respectively. The Mothership may be slightly better after this but there won't be a visible bonus as there was with the previous two transports. By this point you will have met minimum crew requirements, and before that Captain Soban should have destroyed all the Vaygr Frigates, at which point he'll head towards the Carrier. The Carrier will begin retreating; Fleet Intelligence will instruct you to destroy the Carrier before it escapes. Send a couple of Bombers there to help Soban out, whilst your Interceptors should clear up the last of the Vaygr forces and then fly back to the Mothership.
The fifth and sixth transports don't need to dock with the Mothership but if they do they will each confer two Elite Fighter squadrons — one will be two Elite Bomber squadrons, the other Elite Interceptors. These are basically tougher, faster, and more powerful than your ordinary versions. These are a nice, free addition to your fleet, but are not vital to victory in upcoming scenarios, so don't worry if you don't get them, but if you can, it's a good idea to do so.
Once Soban and your Bombers have destroyed the Vaygr Carrier, the mission will end, and the Mothership will warp to Sarum, where there is a Shipyard you intend to use to help rebuild your fleet.