Answers here are all over the map, partly because people seem to be telling you what they'd buy and not what you ought to but, but partly because your description of what you are shooting is ambiguous. So let me take a couple of guesses.

"outdoor/landscape/nature" can mean a lot of things. Since you talk about the super-telephoto range lenses it really sounds like you're thinking wildlife first, landscape second. So your primary lens need is super-telephoto (> 200mm) but you need wide angle as well. That pretty much sums up my photography -- lots of birds, lots of critters, some landscape work, and people only by accident or when forced to.

If that's what you do, you can't do it with one lens, not with any quality. You can cover the range well for $2500. If you are willing to spend some more, you can cover it VERY well.

For a long time I shot with a 24-105 (which others have suggested) and the 100-400. You can buy both of those new for right around $2500. If you buy the 24-105 used (and really good copies are available at a good price) you can hit that number. you have to be careful about buying the 100-400 used; it's a lens that can lose sharpness as it ages and gets bumped around. Newer units seem both sharper and more resistant to that, older units can meet Canon's standards but not be as good. So be careful and test before committing. Or buy new.

Willing to spend more for a better set? Again, I like the 24-105. Buy a 70-200 F4 to cover the medium telephoto, and then buy the 300 F4 and put a 1.4teleconverter on it (I like that better than the 400mm lenses. a bit more flexibility and I think it's sharper with faster AF). That'll run you about $3500 new, but some used shopping will get that down to about $3000. The 300F4+1.4x is a great bird/critter lens, about the best you can do without spending LOTS of money.

Next step up: 24-105, and the 70-200 F2.8 IS II (NOT the older IS). Add a 2.0x III teleconverter, and that turns it into a 140-500 F5.6. That combo has speed, fast AF and sharpness to die for; it's well beyond what the 300F4 can do and blows away the 100-400. It'll also cost you $4000 new for the pieces and the lenses weigh like a brick. (NONE of these combos are light). However, the wquality of the imagery is superb. It's what I upgraded to a few months ago, and the 70-200 just blows me away. It's new enough that there is effectively no used market for it, so it's hard ot shave price here, but I love the results.

The sigma 50-500 gets raves frmo some and criticism from others. It's soft at the telephoto end, but all zooms soften at the telephoto end. Whether it's TOO soft, you'd need to test, but it's an option. But you still need a wide angle, 50mm isn't wide enough for good landscape work. You'll find 24mm on a 7D will make you wish for even wider stuff, trust me on that. (hint: resist the temptation and learn to stitch panoramas. Take shots with the 24-105 on vertical -- spend the money on a good tripod and head instead of pushing yourself to something like a 10-20mm, or consider adding a full-sized sensor like a 6D.

Before you spend money on ANY of this -- rent it or borrow it, take it out and try it. Test it hard. You really, really don't want to spend this kind of money on a lens you decide you don't like. Take some time, figure out what works for you, THEN buy. If you're new to all of this, seriously consider buying the lower end lenses and consider upgrading in a few years; the used market can be your friend here for selling off and upgrading.

Also before you consider buying really expensive lenses (like 500mm or larger, $5K or more expensive beasts), realize that (like avoiding buying the wider stuff by going to panoramas) you can crop images off of a 7D, or you can consider buying a higher megapixel body for a LOT less than these big-nasty lenses, and with some thought and some cropping turn out very high quality work. Modern digital technology gives you options beyond just buying more expensive lenses if you learn how to take advantage of what you can do.

Lots of options here. Take your time, rent and test. Figure out which lenses work best for you. Don't spend the money first and regret the purchase. A rental or two to avoid a mistake is a great investment. Or find photogs around you that you can borrow a lens from or go out shooting with and try things out. These aren't trivial investments. you wouldn't (I hope) buy a car without a test drive. These lenses are like that.