Lots of great advise given by folks here from people with a lot of experience themselves to include Panda Bear and Hunting Wife. You ladies always provide great advise especially when it comes to helping us out with our better half!
1. The Weatherby and Tikka's as listed would be great rifles. Let her pick the one she likes and that feels right for her in that it just fits her. Let your wife handle several different rifles although it looks like she is leaning towards the Tikka. 7mm-08 is a great cartridge especially loaded with a 140 gr. Accubond. I'd suggest taking her out quite a bit with a .22 rifle that shoots well before you let her shoot the Tikka in 7mm-08. Even when shooting the .22 LR have her (and you) wear ear protection. Shooting at paper and shooting at close distances, say 15-25 yards to start with would help build confidence especially when she can see that she's shooting pretty nice groups that are consistent. After she's gotten it down to where she's shooting pretty good, let her start to shoot some reactive targets. You can take a 22 and do it with her at the same time. There are many simple metal swinging plates and such that are just perfect for this. Paper will get boring fast and the reactive targets are a lot more fun. It doesn't have to be elaborate or expensive. As stated by Panda Bear, a good fixed power scope like a 6x42mm or 6x36mm Leupold is a perfect scope. Great glass, strong, and each and every time she pulls the rifle up it looks the same down the scope. Hard to beat it for a hunting scope by going fixed power.
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When she is shooting her hunting rifle I would suggest at least to start by having her use soft plugs underneath a set of ear-muffs. I think it especially helps a new shooter so they don't develop a flinch or reaction to the loud band. Heck I frequently do this myself as it just makes it more pleasant to shoot.
2. Prois has clothing specifically for females as does Sitka.
Keep her warm and keep her dry. It's worth it to get quality clothing and boots. If your wife starts getting cold when you are hunting it's nice to just find a place and sit for a while and start a fire to warm up if conditions allow such to take place. If it's wet and miserable or cold and blowing, you know that you will soldier on because it's hunting and we love it and we will tough it out. Don't do that if you are hunting with your wife! There may be times that it's unavoidable, but at first if possible try to pick the nicer days to hunt with her when starting out.
3. Even if you aren't seeing the game you are after just seeing any other game animals or birds makes it a lot more fun. Worth the price of admission is what I call it. Seeing game and at least seeing tracks or other signs of game sure helps to keep spirits up. Some of the scenery and other things along the way make for some great experiences. Sounds like caribou would be a good starter, as are pronghorn antelope depending on where you live and if that's available. You really don't even have to be up and hunting at the crack of dawn when hunting antelope, and they are a kick in the pants to try and sneak on and get close to. I have not hunted caribou, but from my reading stories by others, that sounds like a good first animal if you are in Alaska. A Sitka deer might be a good one too.
Keep it fun and enjoyable if possible.
Keep your wife fed, warm, and dry. If after a couple days straight hunting and she isn't really into getting up early the next morning then don't. Enjoy the trip, that's what you are out there for. Yes of course some great tasting meat would be awesome too. I would suggest that on the first animal at least, that unless she really wants to dress her animal out, then you do it and just let her help you and see how it's done. Try and help her get her animal first even if that might mean you have to wait a while, or even quite a while. When my wife was hunting with me it meant way more to me that she got a deer or other animal before I filled my tag. Take lots of pictures at camp, while hunting, and if and when she is successful. Say she shoots a nice nice caribou or maybe an elk. Think about surprising her by taking the antlers and displaying them on a plaque or something for her that makes it just that much more special, and which she can look at and remember the experiences you guys shared together, and she can be proud of her success by honoring it for her. If it was an elk they make some awesome necklaces and earrings out of the elk ivories!! That would be something pretty neat to honor the animal and the hunt for her.
As others have said, let her help drive the hunt too.
Some great advise about letting her be a part of the team and deciding where you might want to go in your hunt, how the stalk might play out, and just paying attention to her and what she wants to do and what she thinks might work. Best of luck and I hope you have a new hunting partner for life. It will start all over again when you have children, and take them out as soon as possible to start them on the path of loving the outdoors.
David