No budget really, willing to spend the money for the right camera. Mostly photos will be taken outdoors with mostly no zoom but on the odd occasion will require a good zoom otherwise I mostly move closer to the subjects that I am taking a photo of as using my iPhone the zoom was pretty rubbish! It will mostly be landscapes that I will be using it for.
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Well my starting recommendation then would be either the Nikon D5200 or the Nikon D5300. Both have an outstanding 24 mp sensor and extremely good dynamic range which will be a nice advantage particularly for landscapes. The kit lens should be sufficient for you when you first get started, and you can always decide what sort of lenses you'd like to add later depending on your individual needs.
I'd recommend a good tripod and a remote trigger as well, they are very handy for landscape shots, it will allow you to do longer exposures and still get a nice clean image. I'd also start doing some reading about ND filters, another handy tool for long exposure shots.
I'm going to second these recommendations.
1. Yes, you could get a better camera. But not to sound condescending...but for someone who is using a camera phone now, plunking down several thousand bucks for a professional grade camera (with the weight and size to match) could be a waste of your money. A D5200 or D5300 is not too expensive in-case you decide this was a mistake. Plus it will do what you've said you want it to do.
2. Something that wasn't mentioned is that the D5200 and D5300 are smaller and lighter than other comparable DSLRs. This is b/c the rely on the lens to have an autofocus motor (most modern lens do). So if you're not used to lugging a DSLR around OR you have small hands or you don't have great upper body strength, a lighter and smaller body is a plus. B/c the best camera is the one you have with you. If it's a hassle to lug around, you won't have it with you so you'll end up shooting...with your iPhone.
3. You said you shoot landscapes. So here are some additional things you're likely going to want to get:
--a neutral density filter or a graduated neutral density filter. These are useful when you're shooting in to the sun (like a sunset/sunrise on the beach) or when you're doing a long exposure in order to blur moving water (like with a waterfall or creek).
--a circular polarizer to go on the end of your lens. A circular polarizer reduces glare and will make your clouds and sky pop. It's also good for shooting fall foliage.
--a tripod. If you get in to landscape photography, at some point you're going to start shooting during the "blue hour" (that's after the sun goes down and the move vibrant colors come out in to the sky). And for stuff like that (or to do selfies of you and the family in front of the Grand Canyon), you'll want a tripod to mount the camera on. They're a hassle to lug around so just keep it in the trunk of your car and pull it out when you're going on a hike or stop where you know you'll need it.
--a good landscape lens. Generally speaking, you want a wide angle lens of sorts (in order to get a vista in). Nikon makes a 35mm DX f1.8 lens. Very sharp, light, small, and inexpensive. Now, if you're going to shoot wildlife, then you'll want a zoom (and probably going out to at least 200mm) b/c that Eagle or Moose isn't going to stand still while you get 100 feet closer.