Why don't you take an Epson fine art/photo printer ? Quality is better and ink become cheaper
So then any printer can be used as a sublimation printer as long as we use sublimation ink? I thought it had to be a special printer?
If you're after an A3 printer at a reasonable price then probably Epson is the best option. You can save a lot of money by using third-party inks instead of genuine inks but make sure you buy them from a reputable supplier with a good track record. You can go the continuous-ink route (CISS) or use refillable cartridges. Both have pro's and con's.
With heat presses it's sometimes advantageous to buy a used press with a good name rather than a new, cheap, unbranded Chinese press.
Whatever you buy just remember that sublimation is very much a 'suck-it-and-see' business. You'll need to do lots of experiments at the beginning, starting with suggested settings then refining them to match your printer, inks, paper, press and substrates to achieve the perfect print.
With regards to graphics software, you'll need software that can manage colours via an ICC profile (which should be supplied to match your inks from your ink supplier). So here we're talking Photoshop or the free Gimp for raster work, or Coreldraw, Illustrator or the free Inkscape for vector work.