There are a few different ways I like to look at this. First, you are weak just starting out. Second, you have a low work capacity just starting out. Right now, you are basically working more on your work capacity, and your strength is just going to go up as well.
Personally, I like getting people some good strength gains before starting to work on their work capacity.
Usually a full body workout
Dumbell Flat Bench
1 Arm Row
Teach Romanian Dead or give stretches and do HS curls
Standing Dumbell Shoulder Press
Maybe a few ab exercises.
3 x 8-10 on all exercises except abs.
And I disagree with the other posters, you arent going to need to be near failure at for a long time, and you will keep getting stronger very easily. Do not push the weight until your form is perfect and your body will not be strong enough to do many exercises well initially especially lat pulldowns split squats and 1 arm rows.
The lats take awhile to get going for some reason and you cannot rush that process. Just maintain perfect form, do basic exercises and enjoy your strength increases. You should also start learning how to squat during this time.
A good routine to follow would be CT's full body example
do this 3 days a week changing exercises every day and rep ranges every day
use 3 sets of 12+
3 sets of 10
3 sets of 8
the reps per set will decrease as you get stronger and you should use certain exercises for higher rep days
For example incline pushups could be on your 3 sets of 12 or more day