Well for most uses a dslr with a good lens should enable you to get some good quality landscapes. The bad news is 2-4ft on the long edge is really quite large and you are going to have to compromise somewhere. I'm not too sure just how big you can go with the size but someone on here should be able to give you better advice on that. With photography as a h. obby there are three major things that cost: your lenses, your processing software and your camera body.
The way I see it you could go one of two ways. Either blow the budget on a good wide angle lens (that will eat up all your budget and some) probably above $400 by itself. Then you have the post processing software, the standard is generally adobe Lightroom and Photoshop (and yes you'll want both for landscapes) though other options are available so that will be at least $120 or more. Then you'll want the camera body so count on spending another $1000 to $2500 on that and you'll see that big quality prints will cost you a big investment. That's not to mention the price of a good tripod, remote shuttter release, ND filters, CPLs and other kit. Sorry, its normally a shock to newbies to actually see how much this stuff costs.
Or you could go the route most of us do and start with an entry level camera and kit lens. Lean how to use it and build up your equipment over a few years. You probably wont be able to get big prints that size to start off with but chances are it'll take a while to develop your skills anyway and get something decenrep. o print and hang. It'll cost you more in the long run this way and you'll gradually want better gear. One good thing though is good glass keeps it's value if it's kept in good condition so buy the best possible lenses you can afford and don't be tempted to think that new lenses are allways better. Often a good lens on a cheap body will out perform a cheap lens on a good body.
The kit lenses are ok, you can get decent quality photos from them if you use them within their limitations, but the bigger you print the more you see the flaws in the lens. dont be afraid to buy second hand either, often you can pick up a mint kit lens for a lot less than the rrp. Its not uncommon to see standard lenses go for £50 or £60 second hand, but good quality glass retain 80% or more of its value.
If it were me starting over again I'd say buy a mint 2nd hand entry level body and lens with low shutter clicks. Then I'd save and buy some really good glass, then I'd worry about the rest. To paraphrase Ansel Adams : your first 100,000 photographs will probably be your worst anyway!