How to endgame without ICC

So basically what I am asking is how would you gear yourself knowing that ICC gear won't be obtainable?

I hit 80 about a week ago and I am off to a good start gearing up through heroics, emblem purchases, faction rewards, etc. I play a decent amount but would probably be considered casual due to I don't raid. It's not that I don't want to or don't know how, I just can't seem to find a guild that raids NA times that isn't already focused primarily on icc10/25 or icc10/25H. Regardless how well I may know fights and how competent a player I am there is no chance in hell I would be allowed in a pug for anything with 4k gs or under and no acheive.

All the guides I read and advice I have been given have 1 goal for me past the obvious stuff like farm toc5 for trinket and stuff I'm already doing. Get T10 gear. Is all the other tier stuff just THAT bad or is it simply obsolete to T10? I mean I have to obtain higher gs somehow so I figure why not pick up a 2 piece or 4 piece of something else rather than a miss match of other emblem epics. I have been planning from the start to swap out my mining/skinning for JC/LW. JC still would have it's benefits for sure but if I can't obtain the desired patterns from raids for LW then why bother? Should I even bother stacking ARP for combat spec if I can't reach enough for it to really shine? I like assassination too but inferior weapons (was able to buy a cheap tankard for MH) prevent it from keeping up with combat for me at the moment.

If anyone wants to throw in their 2 cents please feel free. Thanks!

First thing you need to do is increase your GS, don't bother for perfect stats (for now).

1) Farm fos/pos/hor hc and VOA10-25, buy pieces from the website with points if needed to replace your worst ones.
2) Farm TOC10-25, buy some t9 with emblems
3) Farm golds and buy some nice 264 gear from the AH.

Keep going like that until you are 5k-5.2k gs. Then download underachieve addon and link fake ICC achievements to enter some ICC10-25 alt run or pug. Try to raid Tuesday evening, some hours right before the reset, at that time raids are more desperate and they will lower their standard to get people to do their run before the reset and not wasting the ID, so getting in will be easier.

Remember that going from 5k to around 5.7k is the hardest part and it may be frustrating, but once you are up there it will be easier and you will get 6k+ faster.

This may be a super late response but I wanted to thank you for the advice. It pointed me in the right direction and I really appreciate it.

No problem man, I'm glad it helped

To your T10 question:
The set bonus on the 2 piece is just really powerful, it gives you a raw amount of energy which is what bottlenecks your dps. Plus, they have the highest raw amount of stats out of any set (duh). You can also opt in to go for 2 or 4 pieces, both routes are pretty viable. And ofc, until you get them, you can use whatever you have access to. But VoA already gives you (Sanctified) Shadowblade hands and legs.
I would also strongly recommend Engineering over LW, so Engi/JC. It's such an amazing profession in PVE that it can't be overstated.
Mining is a good source of income, and keep in mind that one of the Rogue BiS items is a BoE on normal mode, so you can look for that chest in AH. It's pricey, but totally worth the money ("Ikfirus' Sack of Wonder).
One way or another, try to reach 5-5.2k gs, this should get you access to ICC alt runs on global. You won't kill much, but for Rogues, the first part of ICC is a treasure cave. Marrowgar drops BiS feet and really good ring, GSB drops BiS Chest and Offhand. Unless the group is completely clueless, you should be able to do the first three bosses with an alt run.

Get a fake achievement addon and try to use that one to get into the raid. Just pray when they inspect you that they do not go to achievements tab but just items.

Also make sure to read wow bosses tactics on wowpedia and such just to be prepared. If you don't know anything or too lazy, well just follow what others do...