I am interested in this system and was wondering which books are essential for getting started?
The Core Rulebook.
there's lots of good, entertaining and useful stuff in pretty much all of the splatbooks, but the core rules are complete in themselves, and the only essential part of the game.
I have to agree: the Core book is, seen from a neutral standpoint, a very good basic book: setting, characters, plots, rules, advancement and adventure. You can go wild with it for a long time.
If you have a setting/campaign specific enemy, the corresponding faction book is of course a good idea, however due to the different editions of FS, it could be that you miss something. And if course FS lives through the magnitude of its different factions and enemies.
Glimpse of the Abyss is very helpful if you prefer a more DnD style campaign with lots of different monsters.
Everything else is candy. 
SYL
Once you're happy and confident with the system, I'd recommend getting all the Faction books (Thorns of the Lotus, Blood of the Valiant, Seal of the Wheel, Seed of the New Flesh and Gorilla Warfare) as these really flesh out the various settings, and add lots of really good archetypes and schticks. Gorilla Warfare and Seed of the New Flesh are also really entertaining reads in their own right.
Golden Comeback also offers lots of schticks - some of them are a bit meh, but others (especially the stat schticks) are definitely what I'd consider a worthwhile part of the game.
Glimpse of the Abyss has lots of great monsters you can inflict on your players, and Back for Seconds is full of interesting PCs - some of whom you'll find referred to in the Faction books.
Elevator to the Netherworld is a useful book if you're spending a lot of time in the Netherworld, but otherwise you can get by with the information in the core book. It's most useful if you're doing much with the Four Monarchs.
Iron and Silk is amusing, but doesn't have an awful lot that creative groups couldn't come up with on their own.
Blowing up Hong-Kong and Friends of the Dragon are avoidable.
Of course, the most essential Feng splat book is Out for Blood, which is free to download! Even that, though, I'd say only start reading once you're fairly happy with the core book.
The core rules as was pointed out is all you need.
I'd get Golden Comeback next as that covers vehicles, and gives lots of fun things.
The various faction books is what you want to look at next.
Get the ones that deal with factions you want to utilize first and/or that have rules that relate to what your players are interested in.
Seal of the Wheel has some refrences to weapons from Blood of the Valiant in it if you look at the new types so get BV first.
When purchasng BV get the Atlas version of it. It has an extra chapter and be sure to check the errata Atlas posted for it.
I good idea on purchase order is to buy the book in the way they were released to avoid the dreaded refrence to a previous published book problem you may run into.
Seed of the New Flesh and Gorilla Wrfare are best purchased together.
Glimpse is a monster book, but it has a bunch of new schticks in it. I mostly use it for the schticks.
Blowing Up Hong Kong is usefull if you plan to set you game in Hong Kong. It does have refences to rules introduced in Friends of the Dragon and Golden Comeback in it so do be aware of that.
The least used books I have are Iron and Silk and Friends of the Dragon. Iron and Silk is definetly the one that just sits gathering dust.
The various adventure books you can get last.
Four Bastards is too linear and railroads the players into accepting and doing certain things. Has a good number of refrences to Golden Comeback in it.
Burning Shaolin - Is doal stated for D20 and FS. Use it if you need to introduce D&D players to FS. The plot of it steal heavily from a very famous martial arts film.
Marked For Death is ok. You can get the adventure Shaolin Heartbreak that is in it online for free on the author's site. The online version has some text in it that got deleted in the print version. This adventure is connected to the one in Seal of the Wheel so you want to run it before that one.
In Your Face Again only had 2 adventures in it that my group enjoyed. Refrences to other FS book pop up in it often so don't get it until you have some of the other supplements.
Bes sure to check out the various Feng Shui RPG sites as they have many things you'll want to have.
If after all this you are still looking for something to get. Try and find a copy of the Nexus RPG as FS mechanics derive from it. The one expansion Nexus Life you can skip as it didn't have any new rules in it.
The old Shadowfist Players Guide may be another thing to look at if you want some pictures of Buro weapons, armor, and some background stuff.