Hiya I am fairly new to illustrator. I have made a logo for my client, which is all vector and ready to handover. I've saved a pdf version and an .ai version to give to him and these are good, but they seem to have a white background on them. I have saved one as a 24bit .png but I seem to lose the vector quality can somebody help me please? what do I need to give him and how? P.S he will use these both for web and print. As he wants tshirts made and obviously no white background!
You should send your client an .svg file, which will save the vector qualities, have a transparent background and canne uploaded to a website as an svg, therefore be live as a vector
If you don't have any white background on your Illustrator file, then there will not be any background on your .ai or .pdf.
If you want to test this and make sure there's none, open your .ai created from your Illustrator software in Photoshop. You should get only one layer with the logo on it only and no background. If you see some gray and white checkerboard pattern in the background, that means it's transparent!
If you want more opinions and suggestions on what kind of files to provide for your logo, here is a question about it.
You can give to your client the .ai and .pdf for the t-shirt project. I suggest you provide some web and high resolution files and not only vectors. This way your client won't need to optimize these files himself and the result might be way better if YOU do it since you're the expert, after all!
You should export an SVG from Illustrator. It is scalable and will always be a good way to show an icon on the web.