Having bought myself a Trek 1.2 myself last year, from experience and what others have also said, I would look at buying new tyres for it and also a set of new brakes.
I found that with the tyres that come with it I was puncturing approx every 30 to 50 miles, that was during the winter months though when punctures are more prevalent, I have since fitted Marathon Plus and am now short of 2000 miles without a puncture. When I removed the supplied tyres I could not believe how flimsy they were.
The brakes are also renowned to be very poor, I put up with them for a while with having a few near misses but it really sinks in at fast speed downhill and you suddenly start running out of stopping space, overshooting junctions etc that you have to change them. If I recall I fitted "ultegra" pads" and that vastly improved things.
As my Trek was a 2008 model the brakes may have been changed but I believe the tyres may be the same.
Overall though they are excellent bikes so it is an good purchase you have made and hope you enjoy it as much as I do mine.