Sorry - this is long, please bear with me
If you're new and on a budget, I'd recommend any of the older AF Nikons , Canons, or similar film cameras. I see people practically giving whole setups away on Craigslist all the time, yet they still are comparable to $1000+ new cameras - just using film instead of a sensor.
For what you want to do, it should work perfectly well and after a couple of years, you can think about moving on to digital or medium format or whatever. First major camera, IMO, should be about as simple and straightforward as possible, and digital cameras these days are anything but that - at least the ones that you can change lenses on/aren't consumer point and shoot models.
People will say go digital, but that requires software and a home printer. If you're looking at NOT printing at home, the only price difference between a lab printing film and digital is the cost of film, which is cheap. As in several hundred rolls developed to equal the cost of the least expensive large format inkjet printer. A typical lab will do identical results under 8*10 to most home units that any beginner would find remotely affordable. For less money. The local one to me does 400DPI Dye Sub 5*7 prints for 35 cents each with the coupon in the local community paper. And no extra charge for developing, either(couple of dollars without the coupon). I can't hardly buy the paper for that cost, let alone the ink or the printer.
If you're on an even tighter budget, you can find any old Canon, Minolta, or similar manual focus film camera. Even 20+ years later, an old AE1 is still more camera than most new users can possibly handle. Tough as nails, too. Probably buy a body in good condition for about the cost of a full tank of gas.
Older manual focus prime lenses are often superb quality and you'll find them at silly prices at garage sales and so on. Even a camera shop usually will have a good price on them, and for what you are doing with landscapes, it's usually a matter of spinning the focus all the way to infinity and playing with the aperture.(auto focus isn't really required for landscapes like, say, sports shots are)
Film also lends itself to a more "art" result. It can do much better color rendition, dynamic range(and shoulder) and make for a more seamless look under the right circumstances. Want 16-20MP quality? Good film can do that.(Fuji Velvia 50 speed side film is a favorite of many here)
I use it for landscapes because I have yet to find a camera under $3,000(used) that does dynamic range close to good film. And for landscapes, low light, and similar shots(macro as well), contrast is an enormous factor.
But it's obviously not going to work for someone making a living off of it - it's slow, cumbersome,, and time-consuming compared to digital. But for someone who wants to do a few rolls of landscapes and the like per year and has the time to carefully set up a shot, film gives tremendous bang for the dollar, even today.
Professional quality film is really quite astounding stuff, since it's basically made from the same stock as motion picture film - which keeps being refined to the point of absurdity. As long as 35mm cinema cameras are made(100+ years I'd wager), film will still be made - it's not going extinct. Just more of a specialty product is all. It's going to be a LONG time every last film is shot in digital, no matter what Lucas says about it.
As for the exact lens, 24-28mm is roughly equal to the look that you see in a typical movie theater(80-90 degree visual width). This also is about as wide as you can get without noticeable distortion. Since most film can be pushed a stop or so now without much problem, you don't need a "light bucket". A much cheaper 28mm/F2.8 or so will more than suffice for most shots instead of a pricey f/1.8-2.4. The same goes for a 45-50mm lens. Canon makes a 50mm/F1.0. (price of a good used car!) 99% of sane people just get the older 50mm f/1.4 for pennies on the dollar. It's a darn fine lens.
Another advantage is that lenses that aren't the super-low-light models are very short and compact, so you can fit 5-6 lenses in a fairly small bag. A 1/2 lb 50mm lens is a godsend on a trip.