The traditional "Hello World" that I learned was to insert a functioning lacZ plasmid into a mutant E. coli strain that had their lacZ gene damaged. When you do this, you introduce a functioning lacZ gene into the E. coli, which will cause the colony to turn blue in the presence of X-gal. It is a nice and cheap way to do screens... but it isn't nearly as cool as glowing super-bugs.
GFP is a fun product to learn hydrophobic column chromatography. I still think it's best to start with nucleic acid separation before protein separation, though.
Aside from yeasts, there's no way you can do Eukaryotic stuff easily. You'd need a laminar flow hood and very sterile incubators.