personally I wouldn't train my biceps and triceps one day and then my back and chest the other.

Especially not in that order...

You're going to fatigue your biceps and then try doing exercise like seated row, pull ups and Lat pull down? Same with your triceps? fatigue them and then try and bench and shoulder press?

You'll be limiting how much you can hit the larger muscle groups because you've isolated the smaller ones and they can't keep up. You'll bottle neck them.

Personally I would train my Biceps and Lats one day and Chest, delts and Tris the other... If you're going to split it like that.

You don't need a whole session to condition your biceps and triceps... they only move one main joint (the elbow) and also your shoulder slightly... you hit them whilst training the larger muscle groups (back and chest) so they're activated any way... so just add some targeted exercises for biceps/triceps into those days anyway.

Not only will you not be able to hit the muscle groups as well but because you're activating the muscles you've just trained the day before at best you're going to prevent them from recovering/growing and at worse you're going to over train and possibly injure them.

Personally I like to train my upper body one day and my lower the other... so I super set (do alternate sets on the opposing muscle groups) and get a good 2 day rest before training them it again.

As for morning running and caffeine, firstly caffeine is little than a placebo when it comes to physical activity... might make you feel awake but that's about it... morning running is pretty pointless really... only do it if you have too.

I'd much rather run once I've naturally woken up and gotten some energy into my system... good luck putting on muscle if you're going to be running first thing after training on an empty stomach... unless you got a lot of fat on you (which at 6 6" and 200 pounds isn't likely ) you're going to end up eating into energy you should be using for muscle growth/muscle.

Plus there's no need to mess up your metabolism and sleep routine... that's gotta be sorted for your body to recover... the training is only half of this game... rest and fuel is the other

Sorry if this comes across as way to critical but it's good to start off on the right foot instead of learning the hard way from experience and mistakes like some of us had to...