In the world of advertising specialty, shirts occupy a special place. This is so because not only are shirts used more often by people for various occasions, but also because they last longer than say t-shirt or other merchandise.
An advertising specialty shirt can be of various types. You can choose to get your shirt embroidered with your logo or message, or get it screen printed, or get it directly digitally printed, or get the message made separately on cloth, which is then stitched on to the shirt. Screen printing, however is not used much, even though it is cheaper. The simple reason is that it does not last long and gets damaged easily (by a hot iron); besides, it does not look as good as the embroidered or digitally printed finish.
The cost of getting such specialty shirts printed or embroidered would depend on the time that you give someone to make it. If you need it at a short notice (there are companies that would do it for you within 48 hours), the price you have to pay will go up. It is, since, best to plan an advertising campaign using special shirts, to save precious dollars. Of course, if you buy the special shirts in bulk, they are cheaper.
Before selecting any company for advertising the specialty shirt, ask for samples of work done or a sample of the work that you want done. No decent company will refuse to do a sample for you.
If you want a sticker printed on the shirt using heat transfer, there are two options. The first option is to look for different vendors, one that makes the stickers and another that makes the shirts. Or, you can simply give the job to someone that can do both. The latter option is better, as it gives the company a better time schedule to work with and all the variables are in their control.