So for some reason I was under the impression that the T3X ctr was a 1:10 twist rate but I'm seeing that it is actually a 1:11 (20"). I'm looking for the most accurate factory ammo for it as I won't be reloading in the foreseeable future. Does anyone have a favorite that they find to be most accurate? Thanks in advance.

Every rifle is different, but here are 4 test targets I shot while trying to determine the same thing for my .308 Tikka CTR (in the first picture...from left to right (the targets are labeled but kind of hard to read): 168gr Federal Gold Medal Match, 175gr Black Hills Match, and 175gr Federal Gold Medal Match).  

All three main groups were 6 shots (even though on the middle target those 6 shots kind of formed two small groups), and the last target on the right also contains a 3 shot group which was done after my testing to zero the rifle with the load I was going to use...I chose the Black Hills 175gr.

In the second picture is the target from the Hornady 168gr BTHP.

Summary:
175gr Black Hills: 0.75"
175gr FGMM: 0.87"
168gr Hornady: 0.88"
168gr FGMM: 1.25"
Sako 150gr SP: 1.30"

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NewBMowner, have you tried any of the lighter loads around 150 grain? I had read somewhere that they performed better than expected (I realize quality varies greatly in that range but all things being equal, I am referring to the grain weight).

The only lighter stuff I have tried is some Sako 150gr SP (hunting ammo)
Here is the result on that one:
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Also, here is another group from the 175gr Black Hills ammo that I ended up sticking with (mine loves this stuff!):
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The choice for me to go with the Black Hills was pretty easy...although both of the FGMM loads were very close.  One thing to consider is that you can often find the FGMM ammo on sale for $20/box...instead of the ~$33/box for the Black Hills.

A lot of people are liking the stuff from Prime.

I started shooting my CTR with Hornady ELD-X with .5-.75" results.  Then I ordered a case of prime ammo and have been consistently getting .5" 5-shot groups.  Went prairie dog hunting at 470 yards with it in 15-20mph full value winds and had good results.  I don't have any proof on me right now so you'll just have to take my word for it, but Prime and Hornady have both done exceptionally well for me by my standards.

I'm in the same boat and don't reload. I'm at a point in my life where I have more money that time. If I reloaded, it would mean less time shooting.

I don't one a Tikka, but I've tested just about everything out there. For 300 yards and in, 168s are typically more accurate. Beyond 300, my rifles have always preferred 175s. Black Hills was decent, but FGMM was better IME.

Federal (FGMM) 168
Federal (FGMM) 175
Lapua Scenar 155 (yes, they offer in factory load 50 rd boxes)
Copper Creek 168
Copper Creek 175
Prime 175

Gmm is consistent and priced right. If you plan to reload, consider creedmoor ammo as it's loaded in lapua brass.

I "feel" like my tikka shoots better clean. I'm waiting until I have a solid handload to see if it's just superstition or real.

I have not tried the Prime yet.  I keep hearing good things though, I guess I need to order some now :)  Seems like it is about the same price as the Black Hills.

This is the thing with factory ammo - you really don't know until you test it in your rifle.

Plenty of factory ammo is "consistent" enough to be accurate, but the question is whether or not it hits an accuracy "node" in your gun. Small dimensional differences in bores and chambers (and thus pressure/velocity) affect this, which is why it's not guaranteed that otherwise identical models will shoot the same ammo well.

Also, you will want to test in "final" configuration (with whatever brake or suppressor you are going to use), since that affects the harmonics.

As an example, I tried several factory loads in an RPR in 6.5 Creedmoor, and it turned out that 120gr Amax and then 143gr ELD-X both shot the best. Until I put the suppressor on, and suddenly the Prime 130gr took the top spot. Without the suppressor, the Prime shoots around 1 MOA. With the can, less than 0.5 MOA. It's not the fault of the ammo.

My R700 with a high-end barrel shoots the same Prime 130gr at just under 1 MOA no matter what's hanging off the end, but the Hornady is better. Again, not the fault of the ammo (but I want to play with length now....).

...this right here ^
excellent summary