Having almost cleared high rank (two quests away), here's what I'd recommend, although none of this is set in stone:
-It's worthwhile to get those ingredient and "farm" expansion sidequests done early. Better food means better boosts for missions, and more slots for multiplying items means less gathering headache later on. You'll also get sidequests that will unlock some additional mantles, which are less important since the health booster is usually the way to go anyway, and you'll unlock that automatically as you progress. But you're going to want to do all that stuff eventually, not a terrible idea to just do them whenever they unlock, since much of it gives immediate and ongoing benefit.
-In general, sidequests that aren't going to get you crafting parts you care about atm, and don't fullfill a request from an NPC, can be ignored. You have better things to do. Likewise, you will be accruing vast numbers of "investigations." These are great for getting additional rewards for whatever target monster you're hunting (and hence are the ones you should grind on when you need parts), but should only be done when you're looking to craft something.
In short, I'd mainline the sucker, but pause to fullfill bounties and requests that will give you an immediate boost. Clearly at points you will want to pause and do some equipment upgrading, but when and how often you do that is highly individual/variable decision. I found myself stopping fairly often to grind out equipment, whenever there was a new piece of armor or weapon that caught my eye. Your mileage may vary.