I am not showing off my creation per se, but I'll try to give you the advice you asked for.
Some general guide first:
1. Don't try to rush T3 after you get to T2. Look at it more in the way of a benchmark: If you get everything together to craft T3 packs, you are "ready" for T3 research. You need more or less parts and byproducts of other production lines, and if you get a steady stream of all of that handled, your factory runs well enough to start into T3.
2. You don't need to build all four ingredients right where your science labs are. The production lines that lead there are pretty long, and it wouldn't be very clever to cram it all in one place. Try to leave space between different parts of your factory. Your oil industry for example will need a lot of room, so plan ahead. IMO, it's better to think of some way how to transport the different goods for a small distance than to wonder how you should put another assembly into THAT mess...
3. You don't need to supply a million human colonists who just crawled out of their ship each with his own stack of inserters. Try to avoid total overproduction. If you produce something into chests, you can click the red cross in the corner and lock some of the slots for the inserters. I don't know when someone plans on using 48 stacks of smart inserters, but I'll recommend locking all but 3-5 slots. It should last a lifetime (and your factories will always produce more if you need them).
Now on to the four ingredients of T3 science packs:
- Steel is the easiest one. You should be able to handle that, else try to do a bit more stuff with T2
- I always build green inserters in some extra corner of my factory, together with every other kind of inserter. You need lots of green circuits for the whole production, and copper cable for that. The other stuff is pretty standard. Don't go overboard by the way with the amount of assemblies you use to craft the different inserters. A T2 assembly should be able to craft nearly two inserters per second, so one assembly per kind should suffice for starters. Better see that you produce enough intermediate products for your assembly line though.
- You need to establish an oil industry for batteries, if you haven't already. They are not that hard to make; you need a few different chemical plants and operations until you get there, but it's really not a line thats too difficult to handle. 1-2 plants should be enough for the task at hand here (one sulfur plant for example should more than suffice in the beginning). Remember that oil uses some space to build!
- Now, I guess advanced circuits are the most difficult of the bunch, and you should prepare to build them in raw masses. Adv. circuits and processing units are where most of your copper goes to in later stages of the game. If you go for advanced circuits, you should already have set up a basic oil industry - you'll need it for plastic bars. Other than that, copper cable and lots of green circuits are needed (you can use them for processing units also; i try to combine building the adv. circuits and the processors at the same place most times).
Now try bringing all single parts together some way or the other
Don't forget, you don't need to automate EVERYTHING from the beginning; you could gather the different ingredients in your factory manually and put it all into a few chests in front of your science pack assemblies. Or, if you already got to that, use a logistic network. If you don't know it: it's little bots flying around transferring stuff for you without the needs of belts. You could tell them to gather all four ingredients and bring them together somewhere. That should give you a much easier time setting up your T3 production.
Hope that helps a bit!
I thought a bit about writing a general beginner's guide to Factorio. If you guys like it, maybe I'll start something.
(A.1) Electronic circuit from (a)Iron plate (b)Copper cable