Best way to print

Interesting question.  Actually, you should have asked that question to your print vendor before even getting started.  A big part of it is their RIP and final output device.  I wonder if the project will be printed on a White substrate?  Is that a Rich Black?  You typically save in whatever version they can interpret.  When you say "close to original", are you referring to the pic of the dog?  The gradients? 

this is a question for your printer. they would give you the instructions as to the format/way they want you to submit files to them.

The best way is to ask your printer what deliverables it wants. Especially important is asking what black they want and file format.

It's also possible that the printer will want the native art files (depending on the type of printing, any special inks, etc.).  To do this, use the File/Package... command and compress the resulting folder before sending.

Our printing company actually uses a custom PDF preset for our in-house files--from our customers, we usually request native Illustrator art with fonts (or text converted to outlines) and links included.

Hope this helps!

Hi. Usually, the best format for print is PDF/X (there are several standards) but it's a good idea ask to the print provider wich PDF/X to use.