Hey Beth, good thing to consider where you're going to process before buying film. Many people seem to forget to do this! There are three kinds of film; C41 (reversal, or print film,) E6 (slide or positive film) and B&W film.
One hour minilabs only process C41 film which is the most common type of film. It is mostly color but there are two 400 speed b&w C41 films; Kodak CN400 and Ilford XP2. These films reverse the image, producing negatives. The chemicals and temperatures for all C41 films are uniform, there is really only one way (generally speaking) to proces C41 film properly. It can be processed at home but this is not as common as true b&w film.
B&W film also produces negatives, which are in reverse (blacks show up as clear on the negative and whites show up as black.) This type of film cannot be processed by a minilab and requires hand or specialized machine processing. B&W film can be processed with many different chemicals, at many different temperatures for many different amounts of tyme. It brings more creativity into the processing and can easily be done at home. You need a professional lab to do it if you're not going to.
E6 or Slide film produces positives, or slides. The images on the film are the same colours that they'd be on the final image. This film was made to be projected by a slide projector but is now mostly used to be scanned and is favoured for it's ultra fine grain and brilliant saturation. It requires a professional lab to process it or you can process at home but is more difficult than b&w.
Cross processing is popular in Lomography. This is where you process E6 film in C41 chemicals or the other way around.
All the places you listed will process C41 film but they would have to maile the other films out to Kodak or Fuji. It's generally better to find a local professional lab and eventually learn to do it at home.
The only problem you're going to have is that the Diana Mini takes half frame photos, meaning that the camera puts two images in the space where most cameras would only put one image (next to each other.) You may want to tell the lab this so they can either scan/print them as individual shots or scan/print them as pairs.
Here are some of my half frame photos:
http://www.flickr.com/photos/johnnymartyr/sets/72157623435380969/
Btw, you may want to try buying Kodak, Fuji and Ilford films at Adorama.com. They are much cheaper and are usually the same films as the Lomo ones, but Lomo just repackages them and raises the price.
Good luck and have fun!