@bigkahuna your profile says you are in Borden, SK which according to googlemaps is 217km from Nokomis, where there is a fantastic 1200 yard range that belongs to the Sask Provincial Rifle Association.
At your first opportunity, contact SPRA and arrange to visit while they are shooting. Spending a day on the range seeing what people are actually using and shooting, talking to real live shooters who are on a range actually shooting at 300y, 500y, 600y, 900y and 1000y, you will learn more than in months and months of online research. It'll really help gel your ideas on what kind of rifle and what sort of setup you might be interested in getting (for example, there is "TR" shooting which is done with iron sights, sling and shooting jacket; there is "F" Class, which is done with a front rest, rear sandbag and optical sights).
For what it's worth, it's not unheard of for a serious visitor to be offered an opportunity to fire a few shots; careful though, if you fire a few bullseyes at a thousand yards you might end up hooked for like....!
You can definitely get a pretty good setup for under $2000; having good knowledgeable advice will really help. It is also possible to spend $2000 on seemingly good gear, only to find out that it doesn't really fit your needs for a whole variety of reasons. If you can pick up a mentor during your visit to SPRA that would really help.
As for calibre, there are several good reasons to choose a plain old typical .308W target rifle, whether you plan on shooting it with iron sights or with a scope. But this is best explained to you by a trusted mentor.
If you want to set up for under $2000, there are a few key decisions you'll have to make in order to meet your budget and to ensure you have a decently good setup when you are done. Night Force scopes are gorgeous and in a certain sense are well worth the money; but a $1500 scope plus several hundred dollars more for a premium mounting system simply will not fit into a $2000 rifle+scope budget. There are intelligent choices that can be made, to get you an "appropriately-good-enough" scope and mounting system. Make sure you find the right advisor.