Wow, that's a lot. Would anyone be able to give me a brief runthrough of what evs and ivs are and how they work?
EVs and IVs have been around since the beginning, although in gen 1-2 they were very different.
IVs (Individual Values) are hidden numbers that make make Pokemon different from on another, they can be from anywhere from 0 to 31, and cannot be changed. They also determine the type of the move Hidden Power for that specific Pokemon.
However, you can influence a Pokemon IVs by breeding (see a breeding guide for details).
You can also use the Dexnav to catch Pokemon with 3+ Perfect (31) IVs, and as of Gen 6, all Legendaries have 3+ perfect IVs.
EVs (Effort Values) are hidden numbers, but can be viewed in Super Training (not the exact number, just a bar/meter type of thing).
Unlike IVs, EVs can completely manipulated. With a Reset Bag in Super Training, you can reduce all EVs to zero if they are not what you want them to be.
Each Pokemon give a certain amount of 1-3 EVs when defeated. They can be spread across stats, or in just one. (e.g. Seviper give 1 in Attack and 1 in Special Attack, while Beautifly give 3 in Special Attack)
However, there are limits. For a single Pokemon, a single stat can only have up to 252 EVs, while the total across all stats cannot exceed 510.
These are just the basics, if you want to learn more,
here is a page for EVs, and
here is a page for IVs.