Maurice,
First off you will need an Epson printer that will print as wide a transfer as you may need. For tiles, mouse pads and mugs a letter/legal size printer will do. If you want transfers larger than legal size for shirts, you will need to move up to a 13" or 17" printer. You only really need a CMYK printer.
There are currently three choices of dye sublimation inks available...Sawgrass, Artanium, and TOG. I would suggest a bulk ink system or refillable cartridges. You will also need dye sublimation transfer paper for your substrates. Some are specifically for hard or soft goods, other work well for either.
There are many choices for heat presses. If you are planning on transfering to tiles and thicker substrates, I would suggest a swing away press rather than a clam shell. Small presses start around $300 and go up! Match your press and printer sizes accordingly.
There are many suppliers for sublimation blanks, just Google "sublimation blanks." There are many choices to consider.
You should also visit
www.dyesub.org. There are lots of good articles and reading there.
Good luck in your venture!