Welcome to the forum, congrats on fatherhood and glad to read you are back to shootin for more fun. That tells me you are succeeding in your long term plans and goals for a happy life. And I'd imagine you are also realizing that the parenthood part, plays a very big part and impacts all the other plans you have made.
Having been down that road myself, it wasn't until AFTER I retired that I was able to buy some of the better made and straighter shootin toys that now allows me to happily reach personal goals at the range. And having said that, I would have to say that the best made, straightest shooting rifle that I have bought in the past 8 years or so, have been Savages. They are, IMHO, the best out of the box and across the counter rifles available in today's market. I will say, I recently bought one of my adult son's, a Remington 700 in .308. He, like you, is raising a young family and has two sons, so money is a concern. I wasn't impressed by the "feel" of the action, but with the right load, man does that baby shoot. Now it definitely ISN'T a competition rifle, but great for hunting, something you apparently seek. And as another replier mentioned, the costs of reloading MAY be a consideration if that is something you do. But because of your hunting desires, a .308/7mm is the smallest caliber I'd go for, although a 30 -.06 might better fit the Elk hunting search. Can't speak to a 7mm as I've never owned one, but hear they are a very fine shooting rifle/caliber. So if I were you, I wouldn't rule out finding a nice, clean and straight shootin used rifle, made by a manufacturer you feel comfortable with. And that search may take a little while, but from the experience you have, you'll know when the "right" rifle comes into your sights.
At any rate, keep tuned in here and best wishes with that young family you've started. Remember they are number ONE on that "must have" list. And remember, like fine wines, some things take time. Good luck on the search and happy shootin!
Alex