I'll be glad to help you out again applefandroid n_n.
I'm going to say IVs take a huge part in Competitive battling as they make up the value of your certain stats.They're hidden from your view,but Pokemon have IV values for each stat-31 in one means you receive a Pokemon for eg. lets say Golem,it will get the highest attack stat possible for a Golem.
If its just for in-game,IVs won't affect you too much at all.For natures it depends on what Pokemon really.If you owned a Staraptor and wanted to EV train it you'd aim for speed and attack,since Staraptor isn't the defensive sort.
So a nature would probably be the same like that-boosts its highest stat then lower the lowest one since it doesn't give much already.For EV training,it is important not to battle Pokemon that have EVs you're not looking for as that messes it up and wastes EVs in a stat you don't necessarily want to train.And like earlier you should train Pokemon in the stats,they're best at.So if you have a speedy attacker,speed and attack would be the ones you'd wanted to train.
EV training isn't easy,but there is a method to make it quicker.You can feed it I believe a max of 10,stat boosting items to make the process faster,then battle wild Pokemon for the rest of EVS.
Hope I helped again,if this was confusing just say and I'll try put it in better words n_n.