Well, kind of keep the overt enthusiasm to yourself, and put it into the job, doing a really good job. This means being safe, not endangering others, making good decisions and the like. Aim on performing smoothly, this is more important than "fast"; it is in fact fast, by default. Think to yourself "smooth" and "grace". that is a good timberfaller, the good days are the ones you have 50% mmore production with 50% less effort.
You'll only need one saw, one in the truck for backup, but its just there in case of some sort of breakdown. Have at least one extra loop for the primary saw in case you hit rock or something awful. And yes, hardhat.
I'm kind of emabarrassed to suggest this, but it sounds like you'll need a dress rehearsal so you don't stand out too much like a new guy- your coming in equipped like you've done this before, better know where you going to hang that tape from than bumbling with it at the tail gate while everyone is waiting on you.
Don't be afraid of asking for help and don't endanger yourself or others. I'd way rather work with someone responsible and trainable than someone with attitude, especially ignorance or ego issues.
Its a great line of work for the right person, good luck. Did I say be careful?