Hi Kris, welcome!!
I think at your age and being quite fit, you can start with weights anytime, as long as you don't start too heavy. But doing push ups, pull ups, crunches and squats would be no mistake, too. But sometime you'll reach a number of repetitions when it's getting ineffective for further muscle growth.
I wouldn't recommend machines, not if you haven't got a health problem (injury). You can start with free weights, but have to be careful with increasing the weights. In the beginning, learn the proper form and start with a weight you can quite comfortably (without reaching muscle failure!) do 15 reps with for 2 sets. Then gradually increase the number of reps (1 per workout) until you reach 30 for two sets. Then increase the weight slightly every other workout while dropping the reps accordingly, until you're at 15 reps again.
For a routine, what you say to this:
2 sets each:
Push ups (when you can do more than 40, replace with bench press)
Lat machine (when you're strong enough to do pull ups, do them instead)
Do this 3-6 times per week, at least every other day.
Yes, i recommend to keep a log. I think it's not only possible, but best to aim for an increase every other day (workout).
When you reach a state where you can't improve anymore, take a break and ask here on the board again
Have success and fun,
love and peace,