I think you're going to need to start with baby steps. I understand the need to work directly on an FTP server in some cases. My parents own a small catering company. I edit their site directly on the server. But most things I do, I've begun embracing Git.
Based on your questions, it sounds like the first thing you need to learn is how to build up a local development environment. Lucky for you, you're doing PHP/mySQL development. Look into WAMP solutions (That stands for: Windows Apache MySql PHP). If you're on a Mac, look for MAMP solutions, and LAMP solutions if you're running a linux distro. See wampserver.com/en/ for more. These are easy to setup development solutions that don't require you to do much php, apache, or mysql configuration to get a working environment running.
Once you get a local website up and running the next big question is this: can you create a local copy of what you've been working on remotely? Hopefully what you're working on directly thru the FTP server is small. If so, copy it down and make the necessary tweaks to get it working correctly (path and database changes in config files for example). These tweaks aren't something that we're going to be able to help with -- it just depends on your code and how it works. This includes copying down the mySQL info (or at least a subset of it).
Once you've gotten that far, now you need to start thinking about changing your coding mindset. Now when you hit save, you aren't saving to an FTP server. You're saving locally. The idea here is that you make changes on your desktop. If you're working on a bug, fix the bug. Then copy up ONLY the files that you've changed. If you're working on a new feature, finish the feature and copy up only the feature specific files. This is where a Git repository comes in handy. Git will track the changes to your files, allow you to commit changes, then deploy those changes (among MANY more features).
So for now? Forget Git. Work on getting a local development environment running. When you've got that working, learn to code locally, then deploy. When you realize how difficult that is to do manually, THEN start learning Git.
If you've read all that and you think, "screw that, I don't have time to learn that much" then here's an alternative solution. If you must work remotely, then download a copy of WinSCP and setup your FTP connection with that. Inside the options for WinSCP you can define what text editor to use for ascii files. Find the path to sublime text. Now, do all your FTP browsing in WinSCP and double click a file. It will open in Sublime Text. Now in ST, you can make your edits and hit save (or CTRL-S) and WinSCP will upload the file for you. This method is what I used before I embraced Git. In fact, I used it with N++ because it was better than the FTP stuff that N++ had.
That's my two cents anyway - everyone works a little different though, so find what's comfortable for you. Good luck!