Xerox Phaser are very good digital printers for this kind of project and they're affordable for the quality and flexibility they offer. They use a solid ink (powder dry ink/toner) technology; the powder is dropped on the paper and then "cooked" to become solid. But they don't produce as much heat as laser printers, that's why they're a good option for sticker projects. Other laser printers can become messy when stickers are used as stock because some part of the glue will stay on the rolls and something the sheet will curl around them. Ideally for any printer, it's better to use a self-adhesive that has a margin with no glue around the edges.
The Phaser can print on pretty much anything including self-adhesive and can use the same stock as the one used for offset printing; therefore it's a lot cheaper and easier to find a great variety of stocks. Papers and self-adhesive can be purchased at any print shop, they'll trim it to the size the machine can print. Some Phaser can print tabloid 11 x 17" and 12" x 18", up to 46" in length (banners). They can also print in duplex even if not commonly used for stickers.
A lot of print shop own a commercial version of these Xerox printers and they all have an economical and high quality print mode to save inks; the quality mode usually prints a very glossy finish and the dry ink is thicker. Xerox cannot print on plastic or vinyl, but they can print on high gloss self-adhesive though. To fully personalize a bumper sticker, it's even possible to print on both sides if the peel-off side isn't too "sensitive".
It's also considered as an eco-friendly printer since it doesn't produce as much waste as a standard Inkjet; each powder ink cartridge can be changed individually and print thousands of copies. Yes they're more expensive than most inkjets or laser printers but the quality is superior and the number of copies that can be done with the toners is also greater. Inkjets can become very expensive because of the small quantity their cartridges can print and the specific paper they need. And laser printers cannot offer the same quality of the solid inks finish. The Xerox machines are a good investment for these reasons.
Obviously, I love Xerox because I know them very well and tested them to the max of their capacity (and fixed them too); I don't want to sound like a salesman but they're often ignored as an option for proofing and quality printing, and they're really superior to a lot of printers suggested here. There's other similar solid ink printers available on the market that are very high quality as well, but their toners are not available worldwide.
Xerox's office Phaser page
There's many kind of self-adhesive and peel-off stickers on the market, and a good alternative to vinyl stickers is the "FasTrack® High Gloss".
Because of the ultra gloss finish, the colors are sharp and bright. As an extra, some UV varnish can be applied on them to protect them from the sun and from the scratches that could peel some parts of the print. This brand of sticker is super thin and the glue is very powerful; they can stick well even if the surface is not totally flat or not very porous, and they're not affected too much by the condensation, water or the cold. Usually, it's a challenge to keep a paper sticker to stay in place on a round or non-porous surface because of the tension of the paper and the humidity; ultimately some corners will start to peel even in dry environments or on clean surfaces. This is something that rarely happens with the FasTrack, that's why it's a good option as labels for bottles.
This brand usually have a black back side that makes it very opaque. It can be convenient if used to cover another label or a misprint, for example. The feel of that sticker is also really close to a laminated sticker or a vinyl. There's a matte version of this crack-n-peel sticker but it's not very convenient for wine/beer labels or bumper stickers, and the finish of the Xerox ink is so shinny that it almost look like a spot varnish when printed on an uncoated stock.
Combined with the Phaser Xerox as printer, the stickers will have a commercial quality; in fact this combo is used by some print shops but the printer is usually something similar to a Xerox Docu print station instead of a Phaser (the office version).
Spinnaker Coating FasTrack® High Gloss Opaque Labels
Spinnaker Coating main sites for other types of stickers and more details
Spinnaker Coating extra datasheet with similar stickers (different colors, durability, etc.)
Regarding the software to use, Illustrator, CorelDraw and Photoshop give the best results, but any other publishing software will do (eg. QuarkXpress and InDesign). The Xerox Phaser has a an internal postscript driver and can print postscript fonts and files perfectly. There's no problems with Powerpoints, Office Word, Publisher and Excel files either. The Xerox drivers can be installed on Windows PC and Apple MacOSX.
If there's hundreds or thousands of custom stickers to prepare then it could be a good idea to do a "reprint" of the custom elements on a base already printed or to use a special software/plugin for variable data.
Selecting the best software and process to use to print the sticker will depend on how many stickers are needed, if the prints need custom design or texts and how fast it needs to be delivered.
Also, sometimes people forget that cutting papers or self-adhesive manually can be a lot of work and another machine might be required for this part; manual paper cutters such as guillotines are affordable but require some patience and dexterity when cutting designs that use double crop marks for bleed. Some heavy duty trimmers are electric, can do a precise cutting job and trim more sheets at the same time but are usually very expensive; sometimes it's better to start small and then invest in a good trimmer. For big batches of prints and to avoid investing on trimming machines, it's always possible to simply go at a local print shop and pay a little fee to get your sheets cut!