One strong point of DSLRs is the wide range of lenses available for them. But a quick survey of some of Adams' books reveals that he favored normal, moderately shorter and moderately longer lenses for most of his most popular images, a range equivalent in field of view to perhaps 28mm through 150mm for a full-frame DSLR. So, you won't need superwide-angles or supertelephotos if you want to be a digital Ansel Adams, but by all means, use those if they better suit your photographic vision. Whatever focal lengths you choose, you'll find options available for your DSLR.
Tokina 100mm ƒ/2.8 AT-X Macro AF Pro D
The lens determines the magnification at the image plane and (along with the image sensor or film size) the field of view, while the camera position determines the perspective. With a wide-angle lens, you can move in close to a subject to render it large in the frame, expanding the perspective; conversely, with a long lens, you can zero in on a distant portion of the scene for a flattened perspective. Note that while shorter focal lengths provide wider angles of view than longer focal lengths, the term "wide-angle" is relative: 50mm is "normal" on a full-frame DSLR, short telephoto on a Micro Four Thirds mirrorless camera and really wide-angle on a 4x5 view camera. The angle of view of a lens depends on its focal length and the format with which it's used. Also note that a lens of a given focal length, focused at a specific distance, produces an image of the subject at a given size at the image plane. That size (magnification at the image plane) doesn't change because you change the size of the film or image sensor. What changes is how much of the image frame the subject occupies. (A 100mm lens on an APS-C camera frames like a 150mm lens on a full-frame camera, but the subject's image is the same size on both sensors; it just takes up more of the smaller APS-C sensor. If the cameras have the same pixel count, this does result in a "reach" advantage for the smaller sensor.)
Adams was concerned with detail, choosing the sharpest lenses available to him. For today's shooter, that means prime (single-focal-length) lenses rather than zooms, although today's better zooms are very good and used by many pros. Today's better lenses have better coatings and less flare than Adams' optics, and recent computer-aided designs and manufacturing also improve performance. The wide-range "superzooms" are quite versatile, but won't give you Adams-esque sharpness (and they distort more than he would have liked). The fast prime pro lenses offer the best image quality.
Adams had vast experience to fall back upon in determining exposures (as he had to when creating his most famous image, "Moonrise, Hernandez, New Mexico"; he didn't have time to dig out his meter as he skidded to a stop in late fleeting light). But he preferred to use a spot meter to make the best use of the Zone System that he developed with Fred Archer. The spot meter let him measure the brightness of individual portions of a subject or scene, so he could determine the brightness range and work out the best exposure. DSLRs have spot-metering modes, and you can use these in similar fashion (although most read a larger area than the handheld spot meter's 1°). But using the camera's meter to measure different spots in the scene means you have to change where the camera is pointed after initially composing your image. A handheld spot meter lets you take your readings without disturbing the camera (and your composition). Adams used a (now discontinued) Pentax digital spot meter toward the end of his career. Today's Sekonic L-758DR and Gossen Starlite 2 offer 1° spot readings along with wider-zone reflected and incident readings and flash metering.
Digital also provides exposure assistance Adams never had: the ability to examine the image immediately after shooting it (on the camera's LCD monitor) and the histogram (a graph that shows the distribution of the various tones in the image, from dark on the left to light on the right). Bear in mind that the review image is a JPEG the camera creates from the raw data, and the histogram is for that JPEG image, not the raw data—but it still gives you a good idea of what you have, and certainly lets you know on those rare occasions when the digital works completely blow out or fail to expose a frame. And note that you always need to use the histogram to evaluate exposure. The image itself on the LCD can play tricks on your eyes, especially in bright and dark conditions.