I need to be able to remotely log into web servers for my clients and edit code remotely. I mostly use this for CSS changes, but also am starting to play with PHP as well. <
There are several approaches to this that are all editor-agnostic.
First, there is sshfs, which is cross-platform and you can install via your OS package manager. A simple approach would be as following:
mkdir -p ~/mnt/server
sshfs user@server.example.com:/path/on/server ~/mnt/server
Afterwards, you have the complete folder structure from server.example.com locally available at ~/mnt/server. Make sure you set up SSH keys to avoid entering the user password every time. You can find tutorials on that everywhere on the net.
For servers that only offer FTP access (shared hosting and the like), you can use curlftpfs in the same fashion.
To close the connection, simply unmount:
umount ~/mnt
For a GUI-based approach, you have several options. There is Transmit (macOS), which features mounting connections as volumes, Forklift (macOS) which is a Finder replacement that can do the same, ExpanDrive (macOS/Windows) and my favorite Mountain Duck (macOS/Windows).
If you plan to move lots of data, especially a lot of small files, Mountain Duck performs the best in my experience.