Embroidery can be tricky, and many use a proprietary format. This often results in greater setup charges, and depending on output this is probably something Dummo or me couldn't do. Again, the fine lines might make it harder, keep in mind this is thread creating the image. Once they have it set up, doing it straight on hats is the best option. Most get the hats dirt cheap in quantities, so there isn't anything to save by making sew on patches.
As with anything, discounts come with quantities. The big places like Vista Print and such will usually have the best pricing as compared to local, but some local places can give a deal as well.
When it comes to SWAG if you can imagine it, it probably exists. Though I spent most of my time in the industry in the larger sized output formats, I did also do some smaller type stuff, and had a friend in the ad specialty market they did all the little goodies.