The art of precision rifle shooting is really a universe unto itself. And the deeper you go, the more fascinating and challenging it gets. Here are my thoughts based on, I'd say, "serious dabbling" with it, via training classes and range opportunities out to 700 yards or 1500 yards, and more. I've done just enough of it to fully appreciate just what a challenge it is and how much goes into it.
The most essential piece of "equipment" is you, the shooter. You must absolutely master the fundamentals of shooting: posture, breathing, trigger control, and a semi-automatic rifle is less forgiving than a bolt action. The best way to master these fundamentals is shoot with iron sights at 100 yards, practicing all the elements of good rifle shooting.
Then, when you are ready, you can think about equipment. Many new PR shooters think they have to run out and buy the most expensive rifle they can find and the most powerful scope they can find and they often end up disappointed.
For distances out to 600-800 yards, a quality commercial .308 rifle will do and it doesn't have to cost a bundle. I'd recommend you put more money into your glass than into the rifle, or...the old rule of thumb of paying twice as much for and optic than you do for the rifle is good advice.
The good news is that the optics out there now are really great values and many recommend VORTEX with its great quality and great warranty. And...you do NOT have to get a super powerful scope, that is, you don't need tons of magnification.
The parts of your rifle you will want to pay particularly attention to are the barrel, a match grade barrel is worth it, then the trigger, a smoothing light trigger, etc.
The ammo is another factor. The super serious shooter will delve deeply into the Vodoo of reloading to get the perfect load to sync up with his particular rifle.
So, having said all that, you can have a LOT of fun and learn a lot with a simple rifle build and glass and good commercial match grade ammo, Federal Gold Match, etc.
I've had various precision rifles and my most accurate was an AI in .308 with great glass. It was capable of putting rounds through nearly the same hole at 100 and could crank them out to 800 all day long (as long as I did my job).
The most fun I've had with precision rifles are my semi-autos. I built a .223 precision rifle, an AR with a 20" Match Grade barrel (White Oak Armory), BCM upper and lower, Geissele trigger, Magpul PR stock, sturdy bipod, good muzzle brake, etc. I was able to set a 10" plate moving back and forth consistently at 700 yards, and the glass was a Vortex 5-20.
Here's a very important point..buy your gear used. Over on Sniper's Hide guys are CONSTANTLY buying/selling gear, from rifles, to scopes, to equipment, etc. It's a great way to get into it and get better gear that you might be able to afford otherwise.
Then, of course, you'll have to find a long distance rifle range, which can be a challenge to find. At our training facility we have two long distance ranges, out to 700 yards, and then out to 2500 (obviously this is used mostly by the SOCOM units that train there and by the real ELD type shooters). But at whatever distance you shoot, you'll enjoy it. Shooting steel is the way to go because much past 200 yards and you won't be able to see hits on paper and at much longer distances, spotting scopes won't do much for you. They work fine with steel where you can see splash from bullet impacts, either misses or against steel.
OK, there you go.