3 Original breeds to create all the following;

[Tom_DarwinNT]

If you are still considering Australorps, their eggs aren't necessarily cream. I have gotten a few that were quite a light shade of tan but most are medium brown. These are the last seven eggs my Australorps have laid.

Ok that’s helpful, thank you. As I only have google and here to compile my info, any and all advice is appreciated.

 

[NatJ]

I assume the Barred rock x Silver laced Wyandotte would be a decent dual purpose bird?

It should be.

 

[BGMatt]

If i wanted to breed birds that would allow me to have the following outcomes;
White Eggs
Brown Eggs
Blue Eggs
Green/Olive Eggs
Sex Link (Red or Black)
Dual Purpose for all if possible.

How many original breeds of chicken would i need to start with? I understand i would need to start with the Araucana for the blue eggs and for crossing with a white and a brown for different colors but i am unsure which breeds would be best to achieve all my goals with as little as 3 maybe 4 original breeds.
I would line breed for the pure bred heritage birds, cross breed for the sex links and easter/Olive eggers.

What breeds and genetics would work best and would it be possible to start with just 3 different breeds?

I live in Northern Australia in the tropics, so birds that are able to handle warmer temps and handy foragers would also be an advantage for the newly fenced areas.

So I took a bit different approach to attacking your scenario. You say the reason for wanting to create a sex-link is so you can sell people good laying birds and be able to tell which are female at a day old, but egg color for that doesn't matter. Well why not look at an Auto-sexing breed or two? Cream Legbars would be your blue egg layer and if bred together are 100% sexable at day old. Rhodebars give you brown eggs and are sexable at day old. Crossing those two breeds would give you green egg layers (these I think would also be possible to sex at a day old as any barred variety is but I'm not 100% sure due to different base patterns). Both of those birds are ok at being dual purpose although a bit on the smaller side. So maybe a white egg layer like a Dorking that is bigger bodied and a bit more meat. That meets all your requirements except a sex-link, but as stated if purpose is to be able to tell 100% pullet from cockerel at hatch, the breeds I suggested would give you two breed in two different egg colors you could do that with.

 

[Down Under]

Hi Tom, I know I am a bit late to the party but you may want to think in a different direction with this being Australia n all mate. I'm in Melbourne and a lot of breeds go off lay over 30 degrees down here so up there you would be having more trouble with heat than us. There is a big difference between Mixed Climate Breeds and Hot Climate breeds so the main breeds that we can get here that can handle the heat seem to be the Ancona, Andalusian, Egyptian Fayoumi, Leghorn, Minorca, Naked Neck (Turken), Sicilian Buttercup and White-Faced Black Spanish as they were bred for hotter climates so they have less down and bigger combs. I can tell you from first hand experience that the Minorca's don't go off lay until it gets to 37-38 degrees and as a bonus they are fairly lawn friendly and great foragers but they are not meat birds at all unless you like it dry and stringy. Another avenue might be to look into breeds that originated in Indonesia, Thailand, Malaysia, Vietnam, etc. and seeing if any of them are available here as they have similar climates to Darwin. You also have Jungle Fowl with their natural habitat being the forrest's of the tropics so they do well in the heat, they are also available here and I have been told that they are delicious if you want to invite them to dinner. On the other hand if you have a big wad burning a hole in your pocket you can build one of the elaborate climate controlled commercial setups and breed anything that you want.
Line-breeding for your pure lines... line-breeding is just inbreeding with a fancy name that will give you a lot of deformed chooks unless you continuously introduce fresh blood (and fresh problems). A good clan breeding system a.k.a spiral breeding system with five clans or more can sustain itself indefinitely without fresh blood and you can select for the traits that you want not what someone else wants.
As for sex links others might have different stories but the only ones that I have had that could handle the heat were New Hampshire x Australorp, those things would lay on a day that was 42 degrees in the shade while almost passing out from heat exhaustion, they would lay through almost anything heat, cold, molt, you name it BUT they were vicious to anything that wasn't the same cross as them and extremely suicidal in that they were constantly trying to eat anything that was deadly for them... The Rhode Island Red x Australorp may have similar qualities but I couldn't tell you first hand about those.
The biggest advice for keeping chooks in Australia that is hardly ever given is that chooks don't like the heat so make sure you have plenty of shade and ice cold water for them when it is hot or you will be trying to work out how to air-condition their whole area.
By the sounds of your question you seem to be new to chickens so it would pay to get yourself a small mixed flock to start with and see how the breeds that you choose do in your area and remember that the same breed of chicken can have different characteristics depending on the breeder that you got them from so if you get birds from different breeders then leg bands and notes come in handy to keep track.