Some folks dislike the T3's aluminum scope rings.  I used them on a .243 and had no problem.  You can find aftermarket rings made specifically for Tikkas from Warne that use the dovetail on top of the receiver.  Just make sure you put the correct ring in front and have the lug fit into the hole.

I believe the only change to the receiver was to increase the size of the ejection port to make single loading easier. 

Get yourself a Pelican case.  They are not cheap, but they are very durable and they are also perfect for rifles that get put in the holds of airplanes.

All of my rifles have slings made by sloganoutdoors (www.sloganoutdoors.com).  They don't slip.

The only accessory I would recommend is some reactive targets if you have a place where you can use them.  The self-healing kind move, while gongs provide instant feedback.  They offer some variety instead of always punching paper.

I believe the T3X has a better recoil pad than the T3s did so no need to replace it with a Limbsaver. 

Let us know how you like your '06.  I have a Winchester 670 in that caliber and although I've been very successful with it, I don;t enjoy shooting it as much as the two Tikkas I own (in smaller calibers).

You want the scope as close to the top of the receiver as possible, which argues for smaller tubes and no rail.  If you're hunting with your '06, a scope with a magnification range of 2.5-8 or 9 power is very adequate and these can be had in tube sizes less than 40 MM.  You might try the factory rings (I assume they still ship with the new T3x rifles) but if you want to use high quality steel mounts, try these http://warnescopemounts.com/tikka-mounts/

Both the factory rings and the Warne rings screw down tight at the sides of the rings.  You do not screw them into the top of the receiver.  There is a recoil lug on one of the rings (front one I believe) that must fit into a receiving hole on the top of the receiver.  It's what keeps the rings from moving all over the place due to recoil.  Look at the photo about half way down this page where Tikka talks about its improved mounting system:  http://www.tikka.fi/rifles/tikka-t3x  It's the bigger hole smack in the middle of the photo.

All good advice above…but the only thing I would add, just speaking from experience… if you plan on using the rifle for primarily target shooting and occasional hunting I would upgrade the rings for repeated range use.  The factory rings are hit or miss with rifles in the 30cal category. I personally have had 2 sets fail or not hold zero so I just stopped trying to work with them.  not too many bad experiences with smaller cals…

The cheapest, best mounting solution I have found is from DNZ…it would serve you well for both range and hunting situations…you can most likely get away with using a low mount with a 44mm objective to bring the scope as low as possible to the bore as mentioned above.
https://www.amazon.com/Game-Reaper-Tikka-T3-Low-Mount/dp/B00403X4AG

The scope you have chosen is a great scope and probably the best magnification you can buy for hunting…I have a 2.5 x 10 Prostaff5 on one of my 308's and it a great bush gun for whitetail hunting.  No issues with close shots, and comfortable out to 400 yards on deer size targets.
At some point you will want more magnification…I guarantee it!

If the new rifle comes with rings I would see if I could use those first.  As a next choice for hunting/target I would use the Warne rings as was suggested.  For the most rugged use I would go with a rail screwed down onto the receiver and rings that clamp to the rail and scope.

As for rifle hard case the Pelican is an excellent choice but if you don't need that much protection there are other choices.  Most outdoors and sporting goods stores have some to choose from.

Something that would be nice to have is a bipod.  Harris is a good choice or if you have some extra $$ then go with an Atlas.

Enjoy!

Something that would be nice to have is a bipod.  Harris is a good choice or if you have some extra $$ then go with an Atlas.

I don't own a bipod but my rifles are mostly for hunting and unless I'm shooting from a bench, I'm shooting prone, from sticks, or more recently from a tripod.  If you only shoot prone or shoot targets from a bench, a bipod may be all you need.  If you need to shoot sitting or kneeling (not uncommon when hunting), then sticks are more versatile, at the expense of some stability.  If you have to stand because you're in tall grass, then I recommend the Vanguard T62 tripod.  It's inexpensive and worked well for me shooting squirrels last weekend.

My bench shooting is for sighting in and testing hand loads.  If you're going to hunt, it's pretty tough to find a shooting bench in the woods.

One thought regarding rifle scope power.  Keep in mind that the higher the power, the smaller your field of view.  One of the things you want to practice for hunting is keeping the power low to find your target, and then twisting the power knob to “get closer”.  Also learn about the markings on your reticle and how they can be used to range the target if you have an idea of its size. 

If the OP is  getting into “target shooting” and then hunting 2nd…the scope magnification is a conversation forsure…2.5-10 is really only suited for 100yrds if shooting for accuracy, meaning groups…if just plinking shooting steel or larger targets then he can get by and stretch that out forsure…but again, its not the ideal choice if target shooting but an “excellent” choice for hunting.

The 4-16 x 44mm might have been a better pick in the Viper HS lineup to get the best of both worlds.
Anyone i've ever known who goes to the range to target shoot does not settle on a low powered scope…they end up buying another scope pretty quickly if they can afford it.

I don´t know what you all mean when you talk about “the factory aluminium rings” but the real “factory” rings are definitely made of steel. Called Sako Optilock.

We are talking about the cheap aluminum rings that comes with most of the rifles…