Hi Lynne, this is unfortunately a huge topic.
Here's what I'd suggest for an easy approach to printing with an online service, keeping in mind the quality error that you are getting and assuming you're sending to a consumer lab (not a pro lab). There's no need to crop first if your online service allows you to choose the size and crop online - most do.
Export specs:
- color space: sRGB
- file type: JPEG
- Quality: 92
- uncheck Resize to Fit. As wobertc suggests, this will export a full size file and then your printing service will either enlarge it or reduce it in size as needed. If you still get messages from your printing service that the quality is poor and can't be printed (meaning your file is too small) then there's nothing you can do except print smaller - you either made a very small crop of a larger photo and don't have many pixels to work with, or you are printing really large. Here's an article I wrote to help users figure out how large they can print, given how many pixels their photos have.
- With Resize to Fit unchecked (or when specifying a size in pixels), Resolution (PPI) has no effect at all - any number will do. (Here's an article on when resolution matters and when it doesn't.)
Regarding printing on your own using the Print module, for resolution use the native resolution of your printer - my Epson 3880 prints at 360, for example, so I use that. To get good quality prints though, there's so much else to cover that just can't be here, such as profiles and color management.
While I didn't reply to this post to promote myself, for what it's worth, all of these topics are covered in depth in my Lightroom: Producing Great Output video series. It doesn't provide quick answers though - it provides in-depth training. I also offer private online sessions.