If you were thinking about going into 1000yd competitions, what would be your gun of choice?
My first target rifle (which I used with both iron sights and scopes) was built on a Winchester M70 long action (bought as a $300 clearance .30-06 from Canadian Tire). To it I added a 30" stainless match barrel, and put it in a laminate wood stock. It worked quite well.
My second target rifle was built on a Musgrave action, which is a single shot target action built in South Africa. It was reasonably state of the art in the 1970s, and while not nearly as nice as modern target actions it is still capable of delivering accuracy that is fully competitive. It also as a 30" stainless barrel, and it sits in a plain wood target stock.
Both of the above rifles are in .308 Win.
If I were to build a target rifle today, I would likely get a Barnard target action, which is available in Canada from Robertson Composites. I'd choose one of their stocks too, and use any good target barrel.
For shooting iron sight ("TR") it would be either in .223 Rem or .308 Win. For F-Class shooting I'd have to decide if I wanted to compete in F/TR class (which is .223 Rem or .308 Win), or if I wanted to compete in F/Open class (which allows anything <= 8mm). For F-Open typical calibres are 6.5-.284, or more recently several 7mm chamberings.
Is that gun of choice also practical to hunt with?
Target rifles are longer and heavier than typical hunting rifles, and they tend to be single shot too. To most hunters they might seem terribly out of place. But they are just unusually long and heavy rifles. I've taken my .308 target rifle groundhog hunting, all 14+ pounds of it, with a 15X scope, bipod, etc. If you wanted to you could certainly take a rifle like this deer or coyote hunting. It would certainly be accurate enough for the task.