Adobe Illustrator is best to make logo and print design because you can resize artwork anytime without being worrying about it getting pixelated. Photoshop on the other hand comes into play when you need to make website design or need to edit photos.
For comparable performance and capabilities and a WHOLE lot less money (as in FREE) perhaps you could consider Inkscape and GIMP. Both are well-accepted by the design community and both have a huge user-base, lots of freely available docs and tuts, published guides available for purchase, and a feature set to match almost everything found in Illustrator or PS.
Here 70% of people saying illustrator and even i also recommended this software to use it for logo design because its a best one to design a vector logo..
Photoshop is not meant for website design. Photoshop is just professional graphic editor mainly for bitmap graphics like images or photographs. For website design there are such program like Dreamweaver.
An image that is generated by a computer called graphics. The pictorial representation and manipulation of data, as used in computer-aided design and manufacture, in typesetting and the graphic arts, and in educational and recreational programs.The best graphic design software programs are those applications used primarily in a professional environment whether that is for in-house graphic design or by freelance graphic designers.
We have used XARA for the past ten years... It is fast, easy to learn, and has the support required to get you up to speed fast. Main site is: xara.com Tutorial site is: xaraxone.com Forum site is: talkgraphics.com
Try Inkscape and GIMP if you're looking to go the free route. Inkscape for vectors, GIMP for rasters.