I currently work from a home office.
Hardware - My primary workstation is a 27" iMac with 16GB of RAM. I have an iPhone 6+ to keep me going on the move. I also have a HP MicroServer running Windows which I can remote into for testing sites on Internet Explorer.
Connectivity - My primary connection is uncapped DSL, I have a capped fibre link delivered via last mile wireless which I can use if the DSL goes down and I have a 3G data contract which I can fall back on if I need to.
Applications - On the design front, I have Sketch, Pixelmator and OmniGraffle Pro. I turn to iA Writer for Markdown and TextMate for any code I want to look at with syntax highlighting. Kaleidoscope serves me well for running diffs on a variety of file formats.
Chair - I have a Black GetOne Highback from Ergotherapy to keep me comfortable and productive.