Create new Adobe Photoshop File automatically creates a file with the proper resolution and aspect ratio and opens the file within Photoshop for editing (File > New > Adobe Photoshop File).
Import existing Adobe Photoshop file either as Footage, which merges the layers or imports a single layer, or as Composition, which preserves layers for editing (File > Import).
Edit Original allows you to edit a PSD file in Photoshop, with all edits to existing layers (but not new layers) automatically updating within After Effects (Select a PSD file in After Effects, and choose Edit > Edit Original).
Illustrator
Import existing Adobe Illustrator file, either as Footage, which merges the layers or imports a single layer, or as Composition, which preserves layers for editing (File > Import).
Edit Original allows you to edit an AI file in Illustrator, with all edits to existing layers (but not new layers) automatically updating within After Effects (Select an AI file in After Effects, and choose Edit > Edit Original).
Premiere Pro
Copy and paste content from Premiere Pro's timeline to an After Effects composition (#18).
Import a Premiere Pro project into After Effects for further editing (#19).
Capture within After Effects using Premiere Pro's Capture function (File > Import > Capture in Adobe Premiere Pro).
Audition
Edit in Adobe Audition allows you to edit an audio file imported into After Effects in Audition, with all edits automatically flowing through to After Effects (Select an audio file in After Effects, and choose Edit > Edit in Adobe Audition).