1. Inkjet or laser. Both are good for this process and both have pros and cons that are different from each other.
Maybe this thread will help you out. Lasers can do dark shirts, but I believe there is an expense involved. There is a link in this thread that goes to that thread.
What is the Quality of Different T-Shirt Printing Methods? A list in general order.
Some say the general way it goes is this:
Inkjet heat trasfers is cheaper to get into.
Laser is considered to be a better quality by some.
2. For inkjet the Epson's are commonly used.
For laser, Okidata is popular.
There are other printers that will work, these are the most common names I see.
If you do searches on the info I gave you, you will return many threads on the subjects. Good luck to you...