What you're asking for is that mythical "be everything, do everything in one piece" rifle. People, especially newer entrants into the LR discipline, have been looking for that one since the days of the
Atlatl.
Can it be done? It
has been done, many times. Can it be done in a satisfactory manner? Maybe; but usually with a high degree of mediocrity. It's a request for a compromise, which most define as something that does everything sorta well, and nothing in a stellar manner. But for a beginner, it's not a terrible choice. It's just that there can be others as well.
Your question begins with caliber/chambering.
Today, it's very easy to get swept downstream in the vast multitude of choices. Ideally, something with a bullet diameter of 6.5mm or 7mm is probably optimal. I like the 260 Rem for the 6.5, but the 6.5CM has a huge marketing advantage over it, and in practice, the differences are negligible. For the 7mm, the 7mm-08, .284 Win, or .280 Rem are excellent candidates.
Yesterday, there was one answer; the .30-'06. Enough gun to master anything that walks the North American Continent. Kicks a lot, but even in the original rifle, the lightweight M1903 Springfield, it was chosen as the most powerful rifle from which the average soldier could sustain repeated recoil. But for small game, it's like taking on a mosquito with a sledge hammer.
1000yd Competitive? Well, look back far enough, to back before the 308, and it was the Palma chambering for all distances out to 1000yd, and far from marginal at that distance. It's certainly more effective at that distance than the 308 being used today. But rules get made by committees, and once made, are beyond discussion.
The reasoning was that the chambering needed to be a military service rifle one and when the USA changed from .30-'06 to 7.62x51 NATO (.308), that die was cast. But the .308 hasn't been the standard service rifle chambering since the advent of the M-16 over 50 years ago, and that reasoning behind the Palma .308 choice becomes somewhat unfounded at best. With the inevitable and impending military phaseout of the .308 altogether, it becomes fallacious in actual fact. The basic reasoning may have been abandoned, itself; I don't really stay up on such things much these days.
So why is all this sidetrack relevant? It's because it's a good idea to choose a chambering that's not obscure or in an danger of becoming relegated to insignificance.
...And why is it also irrelevant? Because the short action chamberings, especially the 308 and its sibling cartridges (7-08, .243, 260, even 6.5CM) are likely to be with us until long after we are all returned to nature as worm food.
...And as food for thought; the .30-'06 has never stopped being every bit as effective as it ever was, and a good look at the gun shop racks shows that they are not dying out at all.
So you'll still have to choose, but I think these chamberings make a good starting point.
Next point, do we want to do it all with a single rifle? I think not, because whatever you choose, the demands of a hunting rifle and of a match rifle are widely different. Weight? they differ a lot. Length? Same answer. Magazine capacity, in practical terms, they differ too. Optics? there as well. The simplest conclusion is that you'll need more than one rifle; and therein begins the mass proliferation mandating multiple gun cabinets.
So we need to stop right there and do more thinking.
What are we hunting? Moose? Prairie Dogs? Something in between? Each will impose an entirely different set of specifications on the hunting rifle.
What competitive discipline will we be engaging within? Sticking strictly with a 1000yd distance, will it be F T/R, F Open, Palma, Service Rifle? Every single one of these rifles are defined differently by hard and fast rules; and of course, there are other disciplines at different distances, too.
What I'm getting at here is that your intentions could need some refinement. Seen from another perspective, the shooting world is a vast one, and there are lots of questions and each has more than one answer. The way I would approach it is to understand that life is long, interests change, and with them, so does one's choice of rifles. At 74, with a fair number of decades doing all this, that is the most important facet to which I can attest.
Consider all these choices as the start of a lifelong expedition across a vast new land. But to get started, you must ford that first stream. The good news is is that you can pick where to make your crossing. My advice would be to start simple, in a shallow place, spend in a thrifty manner, and make your choices as the most basic core upon which the bigger adventure can grow. Basic rifles support basic learning, and more advanced rifles only become truly useful once the more advanced skills have been acquired. The best gear is best off in the best hands, and so few of us actually fit that mold. Look at it as though you don't tell the rifle anything; it's the one that does the important tallking about what needs improvement.
We can all remember our first rifle. If it was a really good choice, we still have it, and we still use it. I'd still have mine, but my Oldest Brother took it 'for safekeeping' while I was off fighting a war somewhere far away, and some years later, it was destroyed in a house fire. Some days, life is
that way...
...And there have come to be others along the way...
Greg