Designing A Website from Scratch â€“ Illustrator or Photoshop?
Would you recommend Adobe Photoshop, or Adobe Illustrator for a professional freelance web designer on a somewhat-low budget with a small but growing client base?
It's like asking "hammer or saw for homebuilding?"
You need both, and likely several more tools.
Photoshop is primarily for raster Images and illustrator, vector. Both are really handy to have. But you don't necessarily need to use Adobe to supply those tools. There are many more options (the GIMP, paint.net, pixelmator, inkscape, corel, etc)