Here are all of the things you'll need for modding the game. You'll want:
These tools are made specifically for EarthBound. By the way, you don't need PK Hack (aka JHack). It's been replaced by newer tools. Everything here is designed to work on Windows, so you might need to put in a bit of effort to make things work if you're on Linux or Mac.
CoilSnake is the main modding tool. It lets you edit sprites, data tables, the script, and the game code (albeit inefficienty for that last one). It's the central entry point to the ROM for you. CoilSnake takes an EB ROM, decompiles it into human-readable formats like images and text files, and then builds a new ROM out of these. It comes with a map editor, but...
...You'll want to use this map editor instead. Though perhaps I'm biased-- I made it myself. EBME can do a whole bunch of neat stuff and really streamlines the map editing process with things like in-program NPC editing and visual PNG importing. It operates on CoilSnake project files.
EBMusEd is-- figured it out?-- the EarthBound Music Editor. It's a little unorthodox, but if you've had experience with something like Famitracker, this should be familiar to you. It operates directly on the ROM, but you can still use it with CoilSnake via the "Export EBM" feature.
One of the only tools that is still pretty annoying to use with CoilSnake. It's the only way to edit (and add!) PSI animations to the game right now though, so you have no choice. This tutorial tells you the specific things you need to do to add your own, otherwise you can just edit existing ones.
You'll use these to edit CCS files and YML files. Choose one from here, or use your own favourite. Document editors like Microsoft Word will NOT work, you need a program that edits raw text, such as Notepad.
Industry-standard development environment for everything ever. As well as this, it's a very capable text editor, and you get things like integrated Git and Github support, which is ideal for collaborating. Bonus: There's an extension which enables syntax highlighting for CCS.
A popular text editor since forever. It's lightweight and easy to use, and has a lot of powerful features. A great program if you don't think you need the IDE works just to edit some text. Bonus: Slightly more powerful syntax highlighting for CCScript.
These ones always throw newcomers a little. You need to make sure that your editor supports "indexed" colour mode (most images use RGBa). This means that classic editors like MS Paint and Paint.NET won't work. Here are some that do:
A pixel art editor that just kinda does the job. It's a little obtuse at times, but nothing to worry about. That's about it -- it's a solid choice.
Incredibly popular with pixel artists. Though the website says you have to pay, you can build the source code yourself for free, but it might take a while to figure that out. Once you have, it's a wonderful piece of software with a lot of powerful tools designed for pixel artists.
Ol' reliable: a full-on image manipulator to rival Photoshop (it's also a great free alternative to that program). Older versions have been reported to dislike indexed images, so make sure you're on the latest and you should be fine.
You can make a hack, but there's not much point if you can't test it or play it. To do so, you'll need a SNES emulator. By the way, don't use ZSNES. It's outdated and highly innacurate.
A very accurate SNES emulator with great debugging tools for advanced modding. There's not much reason to use anything else.
A little faster, but with no debugging tools. If you're modding on a low-end system, go for this if Mesen lags a little. Also, the fast-forward is a little faster, which is nice for skipping cutscenes and other sequences.
A multi-system emulator with a focus on accuracy. I've never used it so I can't testify about its quality, but other people have recommended it.
You don't need to download any of these right now, since they're mostly only used for specific and often rather technical things. If or when you need them, here they are: