With it being 48 hours since the Commodore announced that the 7th I.T.S. would be taking the tour the galaxy challenge, I include my build so that others can have an idea on what to get/do for it.
I use a Risian Corvette (give away ship). But, you can use any escort because of it's better handling characteristics, an Obelisk warp core (free), the lead foot trait (1.4 to 3 million EC depending on how you catch it), KHG adapted shields and impulse engine (Omega rep), and diplomatic immunity (diplomacy tier 3 and up).
I ran the tour today and here's my results: Sector travel speed 17.08, transwarp speed 34.16 with about a 1.25 minute cool down between activation (estimated because the timer subsides and the button turns green, but the CD is still active and the drive won't light until the full CD has expired).
My driver coil is only 3 at the moment, but I am planning a respec on my toon and upgrading it to six. I am also planning on upgrading to the Borg Assimilated impulse engine (Omega rep) as soon as I have the dil.
During my run I completed the Beta quadrant and transferred to Defera by transwarp and hit five more systems before the mission timer expired. Total take was about 750,000 EC. Not bad for 15 minutes worth of effort. That's what makes this daily so attractive.
Hope that this helps.
Gorgas/Richter