Standard logo dimensions and format?

Hey is there any standards I should know about when designing a logo i'm making a website for someone, i've gotta pretty kickass logo design going but i'm constantly redoing it when I have to resize it for different situations and I know this can't be right..

What are the dimensions for making a logo for the first time in photoshop?

Do you make it over (Re-write text for example) to cater different dimensions? I now know that merging and converting to a smart object gets rids of allot of pixillation but it can still only be stretched so far before looking blurry.

Is importing into illustrator and making a vector better?

This logo will be printed on clothing as well as being displayed in a range of sizes on pamphlets and the website.

Thanks!