Ok, thanks. This is a general outline of what you'll need to start off in sublimation without breaking the bank. Once you start bringing some cash into your business then you'll be able to explore other (usually much more expensive) avenues.
1. A printer. This needs to be able to handle the special sublimation inks, so not any printer will do. The printer needs to have piezo heads so mostly Epsons. I myself have a couple of Ricoh SG3110DN printers which I find excellent, but you may want something larger than A4.
2. Inks and paper. You need special sublimation inks and paper. Don't believe everything you read about Sawgrass being the best option, there a some good, inexpensive inks available that do an excellent job. I'm in the UK and recommend Inktec or City Ink Express inks but do a bit of research to find the best options for your part of the world. Same with the special sublimation paper you'll need.
3. An ICC profile. To enable your printer to print the correct colours that, when sublimated, produce the colours of your design, you need your graphics software to load and use an ICC profile. Such a profile should be supplied by your ink manufacturer to match your printer ink and paper combination.
4. A press. Some of the cheaper presses work quite well, or consider second hand. I'd recommend getting a swing-away press, plus you'll need a mug press or oven to do mugs.