Sights are extremely important too. A match rear aperture (which is much smaller than issue) will enhance sight picture significantly. A 16" barrel will give you are very close sight radius and will make it somewhat harder to get good repeatable sight picture. A rule of thumb so to speak is the further the distance between sights the more repeatable sight alignment will be attained. If you go to Camp Perry you will not see one 16 inch barrel on the line.
Age has alot to do with it as well. After you hit 40 your eyes will change and chances are iron sight shooting will become increasingly harder. You will not be able to focus on front sight and the older you get the further away the front sight needs to be.
Case in point, you don't normally see people over 50 shooting black gun in matches. Space gun yes but not A2 configurations.
If you are not into competition and just want something to blast with a good scope (unfortunately this now means expensive) will be required. Scopes can make you or break you and they are not all created equal.
Another rule of thumb is optics designers are not competition shooters and the internal design/fabrication is iffy at best. The cheaper the scope the less you want to be changing windage and elevation as the mechanisms won't take the wear. Alot of the cheaper scopes are fabricated to allow movement just long enough to sight in once or twice and not move it.
I would check out the warranty of any scope you think about BEFORE purchase. Also make sure it is easily repaired in the US.
You can check out scopes as follows:
Zero at 200 yards for point of aim point of impact POA/POI and fire a new five round group on target. Next move scope 20 clicks right, then 20 clicks down, then 20 clicks left, and lastly up 20 clicks and fire another round in the group. Next 20 left, 20 up, 20 right and 20 down and fire another. Continue on until all four quadrants have been done and if you have a good scope your original 5 shot group should have have increased significantly. If you have shots way out of the group the adjustment mechanism is lacking. In short if your adjustments can't be relied on you don't have a good scope and unfortunately I would estimate 95% fall into this catagory.
The top target scopes in this country are not seen on ARs and no longer made. Unertl and Lyman SuperTarget Spots are the ones I am referring to.
Finally a good match trigger will also help. A two stage match design is critical to repeatable let offs.
As indicated above 1.5" is attainable at 300 with the right combo. A good AR will keep all shots in E target at 600 all day if you know how to read wind/mirage. And perhaps 800 yards you can maintain E size groups.
Go to http://www.1320.us/target/ and you can pull up a nice little target to try your combo on. I would download it on a disc and take to Staples/Office Depot etc and give them the disc and have them print you some. If you have the room/time/equipment you can put one of these up at 100 yards stapled in such a way that the bullet will touch nothing behind the target to deflect the flight. Then at 300 yards place another target aligned so same shot will go through it. That way you will get double prints of group capability at both ranges. Even better do 100 and 600 yards. Warning: don't expect a 1 inch group at 100 to give you a 6 inch group at 600. I believe you will find the average group at 600 will be in the range of 125 to 150% of the close range groups or 7 to 9" at 600.
I take Corplast (political signs are made in millions of this stuff) and politicians love for folks to take them down after election, especially the ones that lose. I have a 4X8 mounted at 300 yards with two 9 inch holes cut so I can put two repair centers over them and the area behind the black is cut away in size of 9 ring. At 600 yards I have another backer target I cover with a "B" target or news print (local newspaper will give you are sell you end rolls of it very cheap) and I shoot at 300/600 with same shots. Old political signs will last about three years exposed to the sun. The take staples well and is the best target mounting material I have ever used.