Depends on what game version you play. In 5.1 or 5.2 before the manpower changes it's feasible (and usually advisable) to conquer all of India before you switch to the Mughals. In post manpower changes, you generally want to conquer as much as you can beyond what you need for the Mughals and then switch to Mughals as soon as you find yourself facing a Tribal Succession Crisis.
Before switching to Mughals don't worry about the other tribes much. They won't pose any real threat. They have crap land so are not worth conquering, however it's a good idea to vassalize the Oirat and Kazahk if the opportunity presents itself (as you won't be able to vassalize them after switching to Mughal). The Golden Horde and Timurids actually often help you with war subsidies and they more than likely will never bother you. And if you get a little lucky the Timurids will indirectly help you by weakening some of your enemies for you. Also push as far into SE asia as you can without getting a direct border with Ming. Get some vassals for a buffer zone there.
Also, take Delhi as soon as you can as it's worth a great deal of manpower and $$$. After that grab Bihar and Kutch asap as they are worth $$$, which you need to support your large army. Be warned that Delhi will spawn some very large rebel stacks on occasion, so when you can station a good sized army there at full moral to destroy any rebels as soon as they spawn.
Before you switch to the Mughals make sure you have a large army, as all your Horde buddies will be your enemy as soon as you do. Only the Timurids will be a real issue though (unless perhaps you pushed to have a border with the GH).
Overall Chagatai is a fun nation to play. It's quite challenging in the later betas, not as much so in the earlier ones or 5.1 once you've mastered how to handle a Tribal Succession Crisis.