is this an image you are going to create in a software program? if so, which one?
if you are creating an image in a vector program like illustrator or coreldraw those programs you don't design worried about dpi as the art is based upon mathematical equations. only when you bring a bitmap image into your illustrator file do you need to concern yourself with dpi and yes the higher the resolution the better.
a bitmap image editing program like photoshop is where you deal with dpi every time you work in it.
you should read up on the differences between bitmap and vector just to get started:
About Bitmap Images - Two Types of Graphics - Vector and Bitmap
read both pages.
as for printing out to film. it's ideal to have an inkjet that uses more than one black ink cartridge. i have an old epson workforce 1100 that does so and it's also wide format at 13" x 19" output capabilities. you have to buy special inkjet film made especially for inkjet printers. you can find this at most silk screen supply distributors online. the reason for an inkjet printer that uses more than one black cartridge is that you want a very solid opaque black so when it comes down to exposing your screen the light is not shining through your design which will make it very difficult to burn a screen correctly, if at all.
if you respond with more details about your project and what you're using we'll be glad to help.
