Which is the best type of printers inkjet, laser, led-lcd, impact, solid ink, dye sublimation?

It depends on your need and your volume. Lasers have sharper text and are generally faster than inkjets. While toner cartridges are more expensive, they print more pages, so the cost per page is lower. But you pay more up front. Inkjets are better for photos and cheaper for low volume. Personally, I use both. I have an inkjet for photos, a color laser for high volume color jobs and a black laser for regular text. I use the black laser most often.
You can get a pretty good Samsung color laser for $ 150 or a really good color laser today for about $ 300. A set of 4 cartridges for the Samsung is under $ 100. Toner cartridges for the other are about $ 200 but they last for about 10,000 pages. You can also get refills for about $ 50 on ebay.
As for inkjets: as someone who was in the computer hardware business for years (though I rarely sold printers since I couldn’t compete with the crazy rebates) I have always recommended Epson. The print quality is excellent, even on plain paper. I have photos I printed on a 640 about ten years ago hanging in my office which still look good, though not as good as the ones from the CX8400 on glossy paper. The warranty is excellent. For a year, Epson will express-ship a replacement and pick up the old one. I had one customer who needed this. He called one afternoon and had the replacement two days later. Another client bought a Canon. It needed two repairs within a few months. Each time it was taken to the repair center, then picked up a few days later. This client runs a specialty printing business and this really hurt. They have since bought an Epson CX5000 and have had no down time since.
All name brand ink is expensive, but you can get cheap new replacement cartridges for Epson (not refills which I never recommend) for under $ 5 at http://ccs-digital.com/ink.asp
The CX8400 scanner/copier/printer was on sale at circuitcity.com for $ 60 with free shipping. It uses 3 colors plus black.
The RX595 scanner/copier/printer also prints on DVDs. It uses 5 colors plus black and has even higher photo quality. It’s on sale at circuitcity.com for $ 80 after $ 55 instant rebate.
http://www.cheapstingybargains.com/54342/epson-rx595-stylus-multifunction-photo-printer-copier-scanner/
If all you want to do is print text, then get a black laser printer which you can find for $ 50 after rebate.