Let me try to answer some of them:
1) Size/Quality: First off for size of the marquee, only you can answer that. I'll assume you meant the dpi/size of the pcitures you are putting on the marquee. I like to go with 300dpi myself. This doesn't mean you can't use lesser dpi graphics that you find. A lot of the arcade graphics are only 16/32 colors, so a lower dpi is fine. It is when you get into grpahics with 1000's of colors and great details that you would want to find 300dpi or better. What I did was create the blank marquee as 300dpi and added stuff to it. You can add a 100dpi picture to it and change it;s dpi to 300 to match the rest of the marquee. Now you can't take a 1 inch 100 dpi image from the net and blow it up to a 8 inch 300 dpi image, it will probably look like crap. So you need to use your judgement on resizng the pictures you find. I've said a lot, but bottom line - go with 300dpi marquee but don't fret about the dpi of the graphics you get from the Net. If it looks good to you, go for it.
2) Printing. I would call where you are going to bring it and ask them what dpi and file format they like. I used Kinkos and printed on backlit film. My Kinkos printed at 300 dpi so I left it 300dpi, and they liked pdf files, so I converted my photoshop to pdf.
3) Backlit - One thing to keep in mind with backlit paper is that the light behind it makes all the colors lighter. Sounds obvious, but it isn't. A black can show up as grey, a dark blue will look like a lighter grey/blue, etc. What a lot of people do (I didn't since my marquee artwork wasn't like this), if you have tru black spaces in the marquee you create a 2nd marquee with just the black parts on it. Let me try to explain, say you had a simple marquee that was all black and them had the word "MAME" in big blue letters. What people do is create a second marquee that was all black but white where the "MAME" letters are on the real marquee (basically a fuill black marquee with the letters/artwork "cut out"). You then place this "mask" marquee behind the real marquee - this way the black of the real marquee gets much less light and therefore looks more black when backlit.
4) Kinkos - you'll see a lot of negative talk about Kinkos. I can't really stick up for them but their marquee printing for me came out great. They also printed my CP overlays which came out with the colors very dull (the main argument against Kinkos). Don't be afraid to tell them to do it over if you do not like the way it comes out. Again, my marquee printing with them was a success - and at about $25 you can't beat the price.