The 6.5X47 is a great round, though I have heard more than once they can be a bit tough to tune.
There are other really good options as well, so if you are open minded and have the time, look around a bit and really educate yourself before making any choices. The cartridge guides are a great place to start, as they will give you an idea of the pro's and con's and also the capabilities of many of the rounds.
As for AI, they are cool as they are different and do give a bit more velocity and less stretching in some cases, but at the cost of case forming. I would prefer a round that has an improved shoulder angle right from the start, as you won't need to fire-form.
Now for other capable rounds to have a look at: the .308, you already have one and it is capable of reaching out a ways and being a lot of fun and accurate. Any of the other .308 based rounds: .260, .260AI, 7mm-08, 7mm-08AI, .25 Souper (308 necked to .25cal), ,243, .243AI, .308AI. They are all decent rounds, and can be formed from .243 or .308 Lapua brass as well. They all have ups and downs, so do some research. The 260 and 7mm-08 can both be very accurate rounds and can be made faster with an AI shoulder. They are also easier on barrels than a .243 or .243AI.
Then you have the 6.5 Creedmore, another good round, though the brass is better if formed from Lapua brass, as the Hornady brass is soft so I am told.
There are also the BR rounds, the 6BR, 6 Dasher, 6 BRX, 6BR-DX, 6BR-BS, and you can also use any of these as a 6.5mm, a 7mm, a .25, even a .22 or .20 or .30 if you want. The .30BR is usually used for short range stuff, but I have read of it doing very well at 600yds.
There is a plethora of good rounds available to reach out to 600-1000yds. Just take some time, look around, educate yourself as much as you can on the pro's and con's of each of them and decide what you want. In the mean time, enjoy the .308 you have. It's plenty capable of reaching out there, and is also great for learning to read the wind. You can also perfect your loading skills as well, as long-range shooting accuracy relies a lot on good loading technique.
And don't get hung up on any one round right away. Keep an open mind and see what you think is going to work best for you. Also remember to consider cost of components, barrel life, ease of finding components such as brass, bullets and powder, and also whether or not loading dies are available or if they will need to be custom. Though with many rounds, such as a 6.5BR, you can use a 6BR die with bushings for a 6.5mm. Some rounds can be loaded in this manner, others require custom dies, so just be conscious of these things when looking at a round. Remember all the costs involved and you will be much happier in the end.
And building a rifle with a round that is easy on barrels is also a good way to start as well. If the barrel is toast in 1200rds, it's not going to be much fun as you will likely be just getting it dialed in and used to shooting at 1000yds and having fun, and now it's toast and you need a barrel. Kinda puts a damper on things for a bit until the new $600 barrel is ready. And it gets expensive as well.

Not to mention many smiths are backed several weeks most of the time, so it's not something you get done on your day off either.
Hope this helps
Kenny