I'll give you my understandign of the subject limited experience.
Breaking in a barrel is basically "smoothing" out the production irregularities in the bore which cause copper fouling. I think the best way to do that is to shoot one round and clean until you see little to no evidence of copper fouling.
I broke in a Sako Finnlight 300 WSM with 13 shots. After the 13th shot, copper fouling dropped off to almost nothing.
Here's another article on barrel/bore maintenance and breakin....
You may not have to do much. My Tikka T3 in 30-06 shot well and didn't foul much right from the get-go. I don't know if ammo makes a difference on breakin, but I would not shoot solid copper (Barnes TSX, etc) right away as they have the potential to foul a LOT. I started off with Nosler Partitions and my first group was under an 1". I was working up reloads at the time, so I only fired 9 rounds each trip to the range for the first 3 or 4 sessions. I think you are OK with firing 10 rounds or so between cleanings, just make sure you clean well in between sessions. That is just from my experience with my Tikka, others may have had different results.
A couple other words of advice for that gun. Get Talley Lightweight (or other aftermarket) rings and screw the scope down tight. I started with the Tikka rings and 1) the drift pin on the front ring sheared right out the front and 2) I couldn't keep the scope in place either. The gun is light and kicks like a mule, even with moderate 180 gr loads, so good scope mounts (and a good scope) are a necessity. You may end up looking into an aftermarket rocoil pad too. I'm not a wuss (or maybe I am) but I have way more fun putting 20 rounds of 338 250gr loads down range than 5 rounds of -06 180gr loads out of my Tikka. The difference is my Tikka shoots 3/4", and my 338 shoots 2", so I take the punishment and leave the 338 in the safe!
Welcome to Tikka. They are fine shooters right out of the box - no Break-in needed. That would be a waste of time and ammo.
You should get under an inch at 100 yards with most any good factory ammo.
I'd go about it more as what performance and projectile you find that meets or exceeds your needs and stick with it. Good ol' Federal Nosler Partition 180 grain is long proven & very versatile loading in .30-'06 with good availability.
The T3 rifles are precisely what Tikka says they are... plan on a lightweight rifle w/ smooth action that is guaranteed to shoot <1" right out of the box. This is my experience w/ all T3 rifles so far --- most achieving under 3/4" @ 100.