Why not forget buying a printer/cutter or anything and start your business by creating artwork, logos and files ?? Put your money to better use and do some upfront advertising and find out what your target audience is going to be. With only $3k to spend, you aren't gonna get jack, so put your efforts into yourself, instead of some useless machine at this point. Everyone is always saying..... ya gotta start somewhere. So, don't jump in the deep end til ya get your feet wet up in the shallow end. Test the waters and prevent yourself some of the miseries we're always hearing about.
It takes more than just confidence, these days.