your question tells me that you have really no idea
illustrator is a complete different approach of graphic design (vector based), and tutorials you need to make your first steps with photoshop won't help you much to get into the world of illustrator (and vice versa).
imho the photoshop software already includes good practice tuturials you can learn from, the main problem for beginners is that photoshop looks very overloaded with so many functions that it's hard to find the tools you really need.
so in your case i would first try to define what you want to learn or what functions you need for the design tasks you have on your agenda. then i guess it's more easy to find the tuturial which helps you with your first steps, if general tutorials haven't done it for you.
btw... if you don't like the idea of buying the software to gain its full support, try gimp. it's free and it offers much of the functionality you have with photoshop:
http://www.gimp.org/