Question
If I am looking to take landscape and wildlife shots and some of those shots being from a decent distance what mm lens would I need? I am not sure what else I should be adding here, I am just looking for decent quality above all else.
Answer
The mm of a lens is the focal length. To take close-up shots of things far away, you need a "long" focal length, which means high mm.
An entry or mid-level Canon camera has an "APS-C" sized sensor. The sensor size is really what determines what the meaning of the focal length is — focal length and sensor size together give you angle of view. (See my visual exercise for understanding that.)
To get another visual idea of what all this means, look at the answers to
How can I visualize or simulate the effect of different focal lengths?, particularly the one that points to Nikon's web-based lens simulator. As mentioned, the numbers are slightly different from Nikon to Canon (choose Nikon's "DX" format to be closest to an entry-level Canon), but close enough that it really doesn't matter for basic purposes. Drag the slider at the bottom to see the effect of a focal length ranging from 10mm to an extreme 600mm.
After playing with that, come back here to read some explanation of what all this means:
Canon's APS-C is slightly smaller than that from Nikon, Sony, or Pentax. This isn't a big deal, but for those systems the numbers below should be a few percent larger for the same meaning. All of the definitions are rough categories, though, so it's close enough that it really doesn't matter.
Anyway, on Canon's APS-C, a focal length of about 27mm is considered normal — that means when printed at normal size, you get a perspective that seems natural and about what you might expect your memory of the scene to be.
Focal lengths in somewhere in that neighborhood are also considered normal: probably up to 40mm or so, and down to about 22mm.
Once you get smaller than 22mm, you're into wide angle. Wide angle won't be terribly flattering for portraits (it will cause features to be exaggerated if your subject is close enough to fill the frame), but the more-normal end of the wide range is pretty common for street photography. And, wide angle is very common for the landscape shots you mention.
Down below 15mm, it's "ultra-wide", where perspective distortion starts to be a key feature of the way the lens sees. This can be used for landscapes, but you have to be very aware of the distortion and the field of view of the lens — see this question on ultra-wide composition.
On the other side, there's the telephoto range. Telephoto has a technical meaning, but generally we use it to just mean a lens with a relatively long focal length (high mm). The range from around 50mm to 85mm is considered short telephoto or portrait — the latter because, well, it's a good range for flattering perspective for portraits, and it's not so narrow that you have to stand hundreds of feet from your subject.
Beyond that is the real telephoto range. This is generally what people want for action and wildlife shots, because they enable you to get right into the action without actually being close.
Consumer-priced telephoto zooms usually go to 200mm, 250mm, or 300mm.
Lower-cost lenses in this range tend to have less ability to let in light — they are "slow lenses". The fancier, "faster" lenses in this range used by professionals and enthusiasts for sports and wildlife cost one to two thousand dollars. And for fast lenses beyond 300mm, you could pay several times that, even.
But that's probably not what you're looking for right now. It might be — one advantage of just getting the nicer equipment to start is that you can forget about buying stuff for a while and just go out and enjoy while you grown into your gear, rather than growing out of it soon and wasting money trading up. So if you know a 70-200mm f/2.8 pro lens is right for you, it's not a mistake to just start there.
However, it's likely that you'll feel most comfortable starting out with a standard two-lens zoom kit. This isn't a bundle as sold by those shady camera stores: it's something from the camera makers. Almost all entry-level SLRs come with a 18-55mm f/3.5-5.6 zoom (note that the numbers go from wide angle at 18mm up through normal to portrait length at 55mm — this is a very versatile range, which is why it's the default). Many are also offered in two-lens kits with a 50-200mm telephoto zoom — or else, a 50-200mm lens is available separately cheaply. Sometimes, there's "upgrade" options like a 55-300mm zoom, also usually of lower-end features and quality for a similarly-reasonable price. You won't go wrong buying a setup like this from any of the top handful of brands.
Check more discussion of this question.
research. But my values are way off. For this image the focal length is known as 18mm but the value I get is 478.634.... 
I extend each one of the 3 sides till they intersect (shown by the green dots). Then using those intersection points I construct a rectangle as shown here 
. Then I calculate the ortho-centre of the triangle. Then using the formula 
. In my application the focal length is simply a value (integer) that is calculated from the square root of the length of the intersecting points (IP1) to the centre, multiplied by the length from the centre to the opposite midpoint (MP2)
