Although what MrNiteOwl said is true, sometimes it's not an option, and hey we've all got to start off somewhere
Good to see you're not trying to overshoot it with cramming loads of fish into a tiny space as lots of people insist in doing with their first tank. I like the idea of a couple of ghost shrimp, and on top of this fish wise.. a lot of people will probably say a male or female betta (which works well). Personally I'd want a bit more in a 6 gallon. If you follow the "one inch of fish per gallon" rule then you have approximately 6 collective inches of adult fish you could stock. A pair of dwarf gouramis, male and female, could work in there, because they only stay around 2 inches, but it depends whether your LFS sells females - a lot don't because they don't sell as well as males due to the lack of colouring.
As for alternatives.. it'd be probably easier to tell you what wouldn't work. Any form of livebearer in a male and female situation would end up with a population boom as they reproduce like mad. Having said this, a few MALE guppies, perhaps 4, could work really nicely because they're colourful and reasonably active. I would suggest the smaller type of tetras but they do like to be in groups of 6 or more and you could be pushing your stocking limit with that. Avoid anything too active, like danios or "glofish", and anything that likes to be in a big shoal.
Now of course, if you had a bigger tank you'd be much less restricted, but I think maintaining a small tank can be just as rewarding. If you haven't got the tank yet I'd suggest looking around for some cheap deals on something a bit bigger, as said Craigslist is always a good start.
Just remember to read up on cycling your tank properly - a lot of books (actually, one I read last night which I considered gospel in my earlier years) and websites, not to mention LFS, only see cycling or decribe cycling as a period of a couple of weeks where the tank "settles", when it is actually the build up of beneficial bacteria in the filter system and on hard media such as stones and gravel. I'm sure MissFishy will stumble acorss this thread at some point, in her sig she has a great site which is probably the most simple explanation of cycling you'll find and will guide you through the process. Hope this helps