OK I seem to get the idea a techmsrine cannot start the game with the iconic techmarine tool, but has to earn it in play, is this correct?

What do you mean by "techmarine tool"? I'm guessing either Servo Harness or Omnissian Axe as iconic Techmarine pieces of equipment, but I might be wrong.

If you meant one of these, then the answer is yes. Techmarines start with one servo-arm or mechadendrite, and have to wait till rank 4 to buy the Servo Harness Integration talent in order to get the rest of their Doctor Octopus arms. The Omnissiah Axe's Renown requirement also puts it out of the reach of a Rank 1 Techmarine.

yes I meant the axe, thank you. I was under the impression that was a standard issue piece of gear for all techmarines given all tech marine mins seem to come with one...