What kind of printer should I get if I want to make prints that are colorfast- things like mini posters, postcards, stickers, etc. I can spend 3 or 4 hundred dollars. I read about some thermal dye thing and some other options... I don't know what to get. Thanks

You really need a laser printer (for good quality postcards and such). If this is for a business, it might benefit you to contact someone like Canon or Xerox and lease a printer from them. It is costly, but once you figure in the cost of toners, supplies and service... it comes out for the best (and cheapest).

Might I suggest Lexmark color printers.

Thermal dye printers (good ones anyways) can be very expensive.
I worked for Lexmark Tech Support for 15 years before I retired in 2005. Execent products supported by actual real people.