It depends on how far into the game you are. Up until level 24 or so usually you only care about CP and if the CP are similar then the movesets. Once you get into the medium to high 20's that is when things start to get more interesting.
Outside of just movesets arenand CP there are also IV'sIVs (Individual Variables) to keep track of. A Pokemon's IV determines its maximum CP, CP per level, and health. However as long as the IV difference isn't too large, I believe moveset takes priority over IV'sIVs because it is more than enough to make up for the CP/HP difference a lot of the times. Another reason why at this point in the game you care a lot more about IV'sIVs is because you have a lot more stardust and can finally justify spending them.
Think of good IV pokemon as a long term investment while high CP pokemon as short term. It's really important to balance out the two. And if you follow the moveset chart you are good to go. Keep in mind that movesets are random after evolving so if you find a pre-evolved pokemon you only want to look at CP/IV because IV's are the same after evolution. Weight/size do not matter at all compared to these other statistics.
Best movesets for each pokemon can be found here. IV calculator can be found here.