What speciffic type of file should i save with no distortion

I remember when customers sized their art before submitting it for print. Those were the good ole days. LOL But nowadays, I practically never get art already sized. So to answer his question, vector files, (Files made in programs like Adobe Illustrator) do not distort or lose quality when you scale them. Raster files, (Files made with programs like Adobe Photoshop) will lose quality when you scale them. If you are working with Photoshop, then you really need to think carefully about the print size before beginning to even create the art. If you start designing at the wrong size then decide later that it is too small, you've made your first mistake thought it may not be a show stopping mistake. You may scale it up and get away with it with no noticeable loss of quality. There are a handful of things that matter. If you don't understand Photoshop and resolution then use a vector program while you learn how to control quality in Photoshop. Once you understand photoshop you can use either program.

I am a print (offset) Art Director /Designer- work with much higher resolutions and stricter rules, but the same holds true.

Ask for a proof, clearly state that any change in size needs to be reviewed and ok'd by you before print. That any change in size that is not proportional will not be accepted ( but you 'd have already seen this on stipulation above). Have them sign something and offer to pay them ONLY if they can follow these simple rules.. wave the signed paper. This is totally within your rights and should be acceptable.

Photoshop can be downsized without apparent loss of detail, however, making a raster image LARGER is an art, there are better ways of doing it then just dragging. There are plug-ins that use fractals/mathematical algorithms you can apply and/or multi-step Photoshop "Actions" you can run to enlarge a raster image and have it look as good as it can, but still, you can't make up real detail, you get basically larger pixels is all.

Vectors output at the maximum resolution of the output device. If it is 3600 dpi printer , then it will output at 3600x 3600 dpi, ( this isn't the same as a final screen ruling, but rather how small a block of toner the printer uses to describe the larger half tone dot- more blocks mean more accurate/smoother sized dots) if 300 then 300x300. they are "resolution independent" being a formula rather than an established field of pixels.

vector files can be resized to a thousand x's it's size without losing resolution.

before becoming a 'designer' in the digital realm you should become familiar with all the different aspects of all printing output choices, especially between raster and vector.

the only real problem with handling and doing work with raster/bitmap files is the size of the file created within such program(s). going huge with your design at a high quality dpi can eat eat up ram like a pig in oil. and if your computer and OS (ram and ghz included) is not up to par you could walk away from your computer for ten minutes to get a cup of coffee and come back and your computer is still manipulating effects or filters.

if you are a newbie to this saving file types really shouldn't be a concern. it should be learning the basics of design|learning tools and techniques|then learning output options.