Atom: I use the Atom text editor for coding. I do theme development using Atom's editor, writing and manipulating css and template files.
Pantheon: I recommend Pantheon for website hosting. Pantheon is an integrated platform for both hosting and managing websites. Hosting with Pantheon offers the fastest pageload times for Drupal and WordPress websites. Their platform also features automated website backups, iron-clad security and easy scaling. It includes automated development environments for coding and multi-dev environments for multiple developers to work on a single code base at the same time. Most of my client's websites are hosted with Pantheon. Clients may still be the "Site Owner" of their website but can add "Michael Digital" as an Ally Organization.
Google Webmaster Tools: This is a valuable tool to learn how Google's search engine indexes and reads your website. Google Webmaster Tools provides you with insights on your website's search traffic, clicks and indexing. It also alerts you to errors you can fix. After publishing key updates, you can even submit your website for re-indexing to Google. You can submit specific sitemap files to Google here, as well. I encourage clients to set this up and explore the interface. It's fairly user-friendly.
Google Analytics: Google Analytics is a must. You can see daily traffic and which which pages and sections of your website receive the most traffic. Making online decisions based on data is key to business growth. You can setup custom goals where you track key actions on your website like contact submissions, sale purchases and free trials.
Drush: Drush is a powerful command line shell for working with Drupal. It comes with commands like making backups, installing and enabling modules, exporting databases, updating the database, clearing cache and many more.
Website Grader: This tool provides recommendations on a website's performance, SEO, security and mobile layout. It's easy to use and free. The recommendations are solid. Enter your website and see the results!
Moz: Moz is one of the best SEO resources online. They offer products, tools and resources on everything SEO. Some of their products are paid. But, they also offer a wealth of free content, resources and tactics to learn and accelerate your SEO.
Basecamp: I use Basecamp to manage project tasks, create repeatable To Do Lists for marketing campaigns and store client collateral. This is more internal. But, I have found Basecamp to be a solid tool for project management of client work and to keep track of active and completed tasks.