Trade companies are always worth it, you can't state all of India anyway until late midgame. For a "perfect" Mughal game i would move my capital to Astrakhan or any Kaukasus province asap, TC India and state all of the ridiculously rich Persian lands - culture shift to Persian included IF that's possible as the Mughals - to collect everything there (with a main trading port). Or go a step further and collect in Constantinople but by then you are already halfway to a WC. Don't take the decision to move your capital to Delhi if you go this route because it will make culture shifting and capital moving more expensive for little gain.
If you don't want to WC you don't even need to take Humanist or Religious Ideas because most of our non-TC land will be Sunni anyway.
I wrote this with a start as the Timurids or a vassal of theirs in mind which I guess you are playing?!