Re: 300 ultra mag at a grand
Questions like this are a bit scary. I for one imagine a clueless guy trying blindly to shoot long. No offence, we all start at the beginning and gotta ask to learn.
Sounds like you need some education, guidance, and experience (something you get right after you need it).
First, 1k requires some skill, knowledge, and a small pile of good equipment. Serious marksmen don't run bone stock factory rigs at 1k, they are rarely consistently accurate. At the least, the rifle should be properly bedded and the trigger tuned. A brake would be a great investment.
Next, there's no telling how a factory rig will shoot. Chances are, if ya gotta ask, it'll outshoot you at the moment. A bedded action, tuned trigger, muzzle brake, and some load work will likely produce a fairly accurate rifle. At least a consistent tool to learn with.
Personally, I'd pick something else to learn with. Barrel life is too short on an Ultra.
As for education,DefensiveEdge.com Long range hunting how to video would be a great start.
To give you a direct answer, a bone stock rig shooting factory ammo would likely group in the 20"+ range at 1000 yards.
Now, I've made assumptions about your education and experience based on the question you ask. No offense intended. Good luck.