Strength training for total beginner

I have been doing cardio exercises for a while, but I am trying to take up some strength training. I find all the information on strength training terribly confusing though...there is so much information out there that there's no information out there! You have to target the right muscle groups, add a certain recovery time between muscle group focuses, consume the proper balance of amino acids, pick the right exercises, and so on and so on. Every time I try to look up just a basic exercise regime, I find articles that list over 50 different exercises and just say "do some of these" with no real guidance.

Can anyone give me some simple advice on basic upper body/core strength training? Right now I do 3 sets of each of these exercises: bench press, lat pulldown, low row, bicep curl, tricep extension, and planks. I choose a weight that allows me to do 8-10 reps maximum in each set, aside from the planks obviously. Is this good? Should I add/remove/change any of the exercises? For references, the gym I go to doesn't have much equipment...it has a bench/shoulder press machine, a machine for lat pulldown/low row, and free weights between 5-25 lbs. It currently takes me ~45min 3x a week for this, with like 1min per set and 2-3min between each one.