It isn't that the stock lens isn't "good" it's that it's designed to be affordable. There's an original 18-55 and then there's a 2nd generation ("II") version -- the optics in the 2nd generation are better, and the "optics" actually
are good. But there's more to a lens than just the optics.
The 18-55 doesn't have a fast/silent USM focusing motor (that would have increased the price). It also doesn't have "internal zoom" or "internal focusing". That means that when you zoom the lens does grow and shrink (usually that's not a big deal) but it also means that when it focuses the end of the lens rotates. That's generally fine for entry level but for photographers using certain types of filters it can be frustrating. For example, if you use a polarizing filter you have to rotate the filter to "tune" the polarity that it blocks. If you then focus or zoom, all of this changes so you have to reach forward and re-tune the filter again (hoping not to disturb anything else.) It's a variable focal ratio lens and, like just about every other entry-level standard zoom in it's class, the focal ratio varies from f/3.5-5.6 (and so do all the others.)
You can get higher end lenses that will have faster & quieter focus motors, the lens wont rotate as it focuses, the focal ratio can remain constant through the zoom range and the lens can collect more light... but all of those features will increase the price tag of the lens. The "optics", however, will not _necessarily_ be better because the 18-55 is already fairly good.
You did specify budget "as cheap as possible" -- and that's pretty much what the 18-55 lens is. It's designed to be decent, accommodate the needs of most entry level shooters, while being as cheap as possible.
Landscapes aren't "action" shots. So the fact that the lens doesn't have lightning fast focusing should be an issue and you probably want to use higher f-stops for landscapes so the fact that it's not a low focal ratio lens wont be a problem either.
For wildlife the lens totally depends on what type of wildlife. This is where a 300 or 400mm focal length lens is nice to have. You don't have to try to sneak up as closely on the wildlife (and hopefully it's not the sort of wildlife that can run faster than you, is stronger than you, and thinks you might make a nice meal.) But it's still nice to be able to work from a distance so that shy wildlife doesn't run away.
The EF 75-300mm lens doesn't have a very good rep. It's the most affordable, but it's not great. The 70-300mm is substantially better, but it's also more expensive... at about $650 for a new lens. You can pick up a refurb for a little over $400.
Canon Direct Store- EF 70-300mm f/4-5.6 IS USM Refurbished
Tamron makes a 70-300mm which competes with the Canon 70-300. According to the-digital-picture, the Canon lens is better and more accurate, but the Tamron is substantially cheaper (although the reburb Canon lens is even cheaper yet.)
Tamron 70-300mm f/4-5.6 Di VC USD Lens Review