I'm going to guess that you had some shitty bars before; looks like you're trying to remedy that by throwing some real cash at the problem.
If you've got $2000 to spend, you'll be able to go near top-of-the-line for all three, although I kinda question the need for a specialized deadlift bar unless you're a high-level powerlifter; from what I've read a DL bar can be quite frustrating to squat or bench with because of the extra whip, so you're really limited to using it for deadlift-only; but hey, if you have the cash, why not?
Anyways, with your budge,t you could spend $800-1000 on a top-of-the-line Olympic bearing bar, probably $500 to get a top-of-the-line deadlift bar, and then $300-400 on a good general-purpose power bar.
I've been training at a CrossFit box for the last several months and have been able to use the Rogue Bar 2.0 and the Rogue Ohio Bar for most of my workouts there. Both seem like good general-purpose bars and have held up fine with deadlifting 500+ pounds and squatting 400+ pounds (on top of whatever other abuse they take during the CF workouts). I haven't seen or used the Rogue Ohio Power Bar (which is different from the Ohio Bar), but from what I have read it is a little stiffer, has a little more aggressive knurling, and functions quite well for just about anything except the Olympic lifts. Honestly, I'm pretty sure you could just get a top-of-the-line Olympic bearing bar from the maker of your choice for your Oly needs, then get an Ohio Power Bar from Rogue, and you'd be all set, even without the specialized deadlift bar.
If you're just trying to get a handle on some of the defining characteristics of barbells, I would watch Rogue's video (features Matt Chan talking through six of Rogue's barbells, just a nice general overview) and also Mark Rippetoe's video on barbell basics. They provide a decent layperson's understanding of what defines a barbell.