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So I have a rather large collection of X-Wing, but I am missing a few ships:

-Rebel Transport
-Hound's Tooth
-IG2000
-Imperial Raider
-The New Starter set (I have the First Order TIEs, but no T-70)

I intend to get the Imperial Raider and the Rebel transport at some point, but how important are Hounds Tooth and IG? Are they truly essential or can I skip them?

Everything's essential...

I don't think that there are any upgrades in those ships (IG, Hound) that are essential that can't be gotten elsewhere.

Stuff that is unique to those expansions:

Rebel Transport has a bunch of X-Wing pilots and Astromechs. The Stress Bot (R3-A2) is the most major one. If you're playing Epic, there are a bunch of good upgrades in here (e.g, Slicer Tools).

Hounds Tooth has Bossk Crew and Ion Projector.

IG2000 has Dead Man's Switch.

Imperial Raider has the TIE Advanced fix, plus a bunch of useful Epic cards (e.g, Ion Cannon Battery).

The Force Awakens core set has a bunch of stuff, but BB-8 and Wired are upgrades that are generally useful on a lot of ships. The new damage deck is the main thing you'll want out of this, but you can probably buy a friend's extra deck.

The two scum ships are skippable if you don't care about the ships themselves.
If you're serious about playing Epic, you really want all the huge ships. There are a lot of fairly basic upgrades that are unique to only one of the expansions.
If you like X-Wings, you want the cards from the Rebel Transport and the FA Core set. You will also want the T-70 expansion when it comes out, for Integrated Astromech.
If you like TIE Advances, you want the cards from the Raider.

The Raider is currently my top priority, followed by the Transport for the X-Wings. How are Bossk and the Ion Projection?

 Corpsman913 wrote:
How are Bossk and the Ion Projection?

Bossk works best with a ship that can fire twice. Right now, the main way you would use him is on a YV-666 in conjunction with Gunner. He'll also be a good choice on Dengar when wave 8 is released.

The Ion Projector is similar to anti-pursuit lasers, but works as a control ability rather than a damage ability. Very situational.

Well, if you have everything else you may as well get IG and Bosssk for no other reason than to fill in the collection.

The core set is key - additional asteroid choices and a new damage deck that you will need to have to keep playing at some point.

Other than that, it depends what you use/like. The Transport is the X-wing update, the Raider is the TIE advanced update.

 Corpsman913 wrote:
-Rebel Transport

Not essential at all unless you want R3-A2. The transport is only useful for epic games, and those are rare in most areas. R3-A2 is incredibly powerful, but you're really buying a ship for one card.

-Hound's Tooth

Not essential. The cards only available in this expansion aren't bad, but you won't miss them too much if you don't have them. The ship seems fairly popular, but if you aren't excited about it right now then you can still win without it.

-IG2000

Not essential, but good to have. It's the only source of feedback array (a very useful card if you play scum), and the ship is one of the best competitive options for scum. The main drawback is that most of the competitive lists use two copies, so it's kind of an all-or-nothing choice.

-Imperial Raider

Essential if you like the TIE advanced, not at all essential otherwise. The title card is absolutely mandatory to have any success with the TIE advanced. On the other hand, if you don't care much about the TIE advanced and you're part of the majority that ignores epic then you're pretty much just buying an empty cardboard box.

-The New Starter set (I have the First Order TIEs, but no T-70)

Essential in the long run, but it's up to you right now. You will need to get the new damage deck at some point, but otherwise it depends on how badly you want the T-70. It's not a bad ship, but if you have everything else you have more than enough options to make good rebel lists without it.

-Imperial Raider
Don't forget about the Emperor! I expect to see Imperial players playing 2 aces and a Palpmobile (I so wish that I had come up with that name) at Worlds in November. I've played it myself and wrecked a couple of guys.

As far as i am aware, feedback array is only available in the Agressor set, so yeah, its essential.

 Crazy_Carnifex wrote:
I don't think that there are any upgrades in those ships (IG, Hound) that are essential that can't be gotten elsewhere.

 BigRedStandingBy wrote:
As far as i am aware, feedback array is only available in the Aggressor set, so yeah, its essential

Currently, yes, but the Punishing One will also have one.