I shoot landscape and cityscape myself
I think there are some essentials that you need right away, and others that you can acquire as you progress.
What you should have now: a camera (well done for ticking the first box!), a lens (I started off with a 18-200mm zoom lens ), tripod and a circular polarizer. Don't forget a software to post-process you images.
To me, these are the essentials for what you are pursuing. Personally, I think a zoom lens is a good start off as oppose to getting a wide angle lens now, which is what most landscape photographers would probably say. Personally, I think a zoom lens has the flexibility to allow you to discover what works and what doesn't and eventually develop your own style. You can then invest in a good lens depending on your needs. For tripod, just get A tripod. For CPL, find one that doesn't give your image a funny color cast. In terms of post-processing, everyone will recommend different software because everyone has their own preference. If you don't like to spend money on that for now, try GIMP because it's free and it's the most versatile of all the freeware (in my opinion).
Things you may need as you progress: A good wide angle/zoom lens, a carbon fiber tripod, good quality ND filters, remote release. You may even want a new camera

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If you're like most landscape photographers, you'll probably be doing a lot of walking/hiking to get to your shooting location - which is why I recommend a good carbon fiber tripod. Apart from graduated ND filters, you may want to invest in a ND10 or ND 16 filter for silky smooth clouds or water. I use the Lee Big Stopper and Formatt-Hitech Firecrest 16 and I couldn't be happier.
I'm sure you'll discover all sorts of fancy gadgets in between that you may find useful, but I think the above mentioned are the must have for a landscape/cityscape photographer.