This may sound strange but the actual chambering is not overly important in a project like yours, there are literally dozens of different chamberings that will work perfectly well for your needs.
The real issue will be rifle design. I always get nervous when I read someone wants legit 1000 yard reach but in a lightweight rifle. These are generally two things that do not play well with each other. A light rifle is just extremely difficult to shoot accurately out to 1000 yards. Not saying they are not accurate enough to do it, just saying that in field conditions, a lightweight rifle is much harder for us humans to shoot accurately at these ranges.
Light rifles generally mean lighter contour barrels, slimmer stock designs and lighter receivers. None of these add up to 1000 yard consistancy for the most part.
It all comes down to what your idea of light rifle is. Personally, I recommend to my customers that they should have at least 10 lbs in rifle weight if they want a legit, consistant 1000 yard rifle. 800 yards, you can get down to 8 lbs or so and yes, it does make a difference from 800 to 1000 yards making that first shot kill, its dramatically more difficult to make that one shot kill at 1000 yards compared to 800 yards.
Everything just has to be perfect for consistant 1000 yard consistancy.
Its hard to build a rifle for 1000 yard shooting that is not built specifically for 1000 yard shooting. Does that make any sense.......
If it were me, putting the bullet on the mark is much more important then anything else. I do not believe in overkill, I believe in putting that bullet into and through the vitals on the first shot.
My recommendation, 7mm RUM, 7mm AM, 300 RUM or 300 AX. If you went with the RUM chamberings, I would go with a Borden Timberline Magnum receiver, wyatts extended mag box, McMillan A-5 stock, at least a #7 contour, heavy fluted barrel, APS Painkiller muzzle brake
For the 7mm AM or 300 AX, I would go with a BAT model HRPIC receiver, the rest the same except for using an HS Precision DM system.
In the 7mms, I would use the 180 gr Berger Hunting VLD loaded to 3100-3200 fps in the RUM depending on barrel length and between 3300-3400 fps in the AM depending on barrel length.
For the 30 cals, I would go with a 208 gr A-Max, 210 gr berger or SMK. Loaded to around 3200 fps in the RUM or 3350 fps in the AX.
These would offer great results ballistically but they are alot of gun, some do not like that. With a proper muzzle brake, recoil will be of no concern.
If this is just to much for what you want, one of the 6.5mm magnums would be a great choice as well. The 6.5mm STW loaded with a 142 gr SMK or 140 gr SMK would be a great choice when loaded to 3300-3350 fps. Less recoil but roughly the same barrel life as the larger rounds and not quite as potent as some of them ballistically.
Simply put, all of these rifles would be around 10 lbs in rifle weight. May be more then you want to pack around.
To be honest, if it is, you may have to adjust your goals to a more realistic level. Say 800 yards or so with a 7-8 lb rifle.
Hope this helps some.