Ok let me preface this by saying this info was conveyed in a PM conversation with Jasneko on the difference between dpi and lpi and what an artist should make them at for submittals. Please excuse grammer and spelling because I wrote it really fast at night when I was tired. It may get confussing in parts but read the whole thing for context. If you have any questions post them in the thread and I'll try to answer/clarify. Enjoi
DPI and LPI are similar in the info they convey but different at the same time. DPI can be thought of as if you drew a grid on a 1 inch square with the amount of pixels (squares) you have on either the x or y axis determining the DPI. So with you settings at 300 dpi your 1 inch square is 300 pixles by 300 pixles or 90,000 pixels square. You need all that info for printing details and smooth lines (300 dpi and above is neccesary for paper printing, shirts can get away with about half that but wo't be as crisp as they could be, plus woot wants them at 300dpi). Most monitors display at 72 to 96 dpi or 5184 or 9216 pixels square. A slight jump in dpi can dramtically increase file size as you see in this math.
LPI works in a similar way but instead of square pixels it uses dots or halftones (same thing) LPI is totally independent of DPI though. You can have a halftone at 30 lpi and 72 dpi or one at 30 lpi and 300 dpi. Whats the difference? Remember that both are using a grid on a 1 inch square to represent their values. The same 30 lpi dot at 72 dpi then is going to look more pixelated (jagged edges) then the same 30 lpi dot at 300dpi (much smaller squares making up the circle so it appears smoother and more round to the eye).
This is important because when printing halftones, especially small ones you want the most perfect circles you can print because it helps to minimize moire (natural screen interference patterns) and other anomolies that appear in screen printing and especially on garments. Having your half tone then at 300 dpi is perfect because the file your working on in photoshop is probably 300 dpi too so thats perfect, any higher then your working file resolution is pointless. LPI is the next issue then. Your lpi value is going to be much smaller then your dpi (if they were the same value then your dots would be made up of single pixels and thus not dot like at all). Paper printing can be anywhere from 55 to 150 lpi or sometimes more, shirt printing though hovers in the 30 to 55lpi range. Woot's not great and or doesn't want to deal with super fine halftones (you need to use higher mesh screens stretched to higher newton values) so I would recommend 35-40 lpi at most, definitely not 60, few printers in the world can print those. Also be aware that in screen printing your press gain is typically 30 percent on halftones so your biggest ones are going to close up on themselves. You will also lose most anything under a 7 percent halftone so don't do too many soft fades, and if you do don't extend them past half an inch or so if they drop below 7 percent (the way your doing halftones it will be hard to measure the value so you'll have to guess, just use you best judgement, a 0% halftone is blank, a 50% halftone is a circle and a 100% is basically a square as it has expanded to touch the halftones around it and create a fill) I could teach about using alpha channels to measure and create halftones but thats for another time as it's pretty advanced.
The last part you have to deal with is angles. Lots of people do them at 0, 45 and 90. Thats ok if they're using big chunky halftones for style, but if your using small halftones for shading and fine color control DO NOT USE THESE ANGLES AS YOU WILL HAVE MOIRE LINES!!! Did I state that clearly enough. Moire happens naturally in any repeating pattern (you get it sometimes while your zooming in and out of PS or AI when using fine lines next to each other and zoom in and out, they take on a check or wavy pattern as the program tries to redraw them) but there are ways to control it. I won't go into the math right now but trust me when I say you want to use angles that are halfway inbetween the angles I said before, so 27.5 or 67.5 degrees.
As I reread through this I can see some areas where confusion is gonna come up, but ask questions below and I'll try to help. I'm busy with work projects right now so I don't have time to retype it all more clearly right now.