I've had and shot pistols for most of my adult life, but never rifles ... until now. My husband bought me an entry level AR15 for Christmas, which is nice but I'm not into all of the "tacti-cool" stuff like most of my friends. I want to take on the challenge of longer range/precision shooting before my 50+ y/o eyes give out on me. Basically, if we all have to bug out to the compound during the Zombie Apocalypse, I want to be the person up on roof.
My plan is to become a proficient as possible with what I have, upgrade it as I go along, then build/buy something once I know what I really want. I don't know if it's a good plan, but it's all I have right now.
So, I figured since I went and set how "English" is spoken here in the U.S., I might as well address the OP in her issue.
First, the AR is a fighting tool. A lot of us use a carbine type to defend the home. That takes practice, so we have to go out and shoot it. Not that it's "Tacticool", rather that it's necessary. Now if you have a standard AR that could be used more for competitions out to 1k. Depending on whether you want to shoot open sights or join in the scope club. As you mentioned your eyes are what's going(?) so stretching out while you can with open sights needs to be addressed soon. Standard AR-15A2's make wonderful training tools which are easily upgraded and rebuilt for good competition (comp) rifles. You can swap lowers to get a better fit and triggers even except in military type comps. You have to have standard issue to compete in those.
For a bolt action open sight rifle, there are a bunch out there, but to get one today, it's more than likely got to go to a gunsmith for some extra hole tapping to get sights that fit your rifle of choice. Some people feel they are just a lot more comfortable to shoot than AR style rifles. I think AR's are just as good for most shooting inside 800 m.
For really long range, you will need a scope. And, that's how those comps are set up. So, to compete you'd have to have a scope. The first thing I would do is go to an F-Class comp and look at the rifles there. Talk to the owners and ask what they like and don't like about their rifles. Most of those rifles are single shot and you may want to look at or read about different type comps like PRS where you need a 5-10 round detachable magazine for the course of fire. In either case the rifle will need good glass with a usable reticle. So, when you talk to comp rifle owners ask what reticle they have in their scope and why they use that. Ask them how they call wind with it. Some use a bare bones fine reticle and call wind using the target. On some days you can't find the lines on an F-Class target and have to guess. That doesn't lead to a good score. So, using a reticle with stadia on the crosshairs is the way to go.
All this depends on whether or not you can get to a decent range with enough distance to satisfy what you intend to shoot. Get on the internet and do a search. There is also a long range forum on Snipers Hide here that you can ask that question. Understand, you can't jump into this wholeheartedly and start seeing success. I takes time and finding what firearm is going to work for you.