Is it different from what someone with Craft (Alchemy) needs to brew Potions?
I know the Formula Book is an essential, but I'm much more confused when it comes to the "lab" items, portable or not. Are these in any way required?
Creating Extracts requires only a minute of free time, a Formula Book, and an Alchemists Kit (or other source of suitable raw materials if your DM is kind). No special environment is required, and the ability to brew extracts to fill unused slots on-the-fly in the field is considered a given for the class, as written. Note that an Alchemists Kit is not an Alchemists Lab, and may not necessarily be assumed to be sufficient for doing things like creating Potions, Poisons, or mundane crafted Alchemical items. It is instead, roughly an Alchemists equivalent to a Wizards Spell Component pouch:
Alchemist’s Kit: An alchemist with an alchemist’s kit is assumed to have all the material components needed for his extracts, mutagens, and bombs, except for those components that have a specific cost. An alchemist’s kit provides no bonuses on Craft (alchemy) checks. (APG, pg 185)
As with a Spell Component Pouch, it can be assumed to be kept restocked by an Alchemist under normal circumstances without maintenance or significant cost. Those extracts with specifically delineated and named material components will need to have their requisites secured and stocked separately, as is usual and customary.
An Alchemist's Kit should suffice for basic crafting while in the field. The Kit won't grant you any special bonuses, but it encompasses all the basic "lab items" you need for creating your tonics. Certain settings may require special tools/locations for specific alchemical creations, but these should be spelled out for you in their contexts.
You could always expand into something like a Portable Alchemist's Lab for an added bonus (+1), or discover/create your own specialty items to improve your Craft(Alchemy) checks.
As a GM, I would allow for quite a bit of "fudgery" if you found yourself in a situation without your Kit but in need of a potion. I would roll for some random, player-unknown side effects of any potions made without the aid of an Alchemist's Kit - my way of interpreting an "impure" crafting result. Other GMs may prefer to require extra checks or to stifle this behavior entirely.
Sources to ponder: