I agree with Dan, keep your gears if you can. It's easy to readjust the shifting system. With the turn of a couple screws you can set up the derailleur so that it only go so far each direction. I wont waste time telling you how, Sheldon can take care of that http://sheldonbrown.com/derailer-adjustment.html
. Also don't forget to check your chain itself, a link or links can be twisted and/or bent which can be hard to notice and easily overlooked causing all kinds of trouble. I ripped a derailleur off the frame and almost got killed crossing the highway due to a twisted chain. That was an extreme case though, the chain had came off and got stuck a block or so before and I was so mad I just ripped it out and didn't think to make sure it wasn't twisted in the process.
Also as Dan said it may just be your shift levers, especially if you have the twist grip style. The twist grip style has always gone bad quickly in my experience but I've never bought or used an expensive bike with nice ones. I like and have never had any issues with this style http://sheldonbrown.com/harris/shifters.html#underbar
and if your lucky your local bike shop may have some used ones cheep. You may want to make sure you have a Shimano cassette first though most bikes do.
Switching to a coaster is a more involved process. You have to buy a wheel and probably a chain too since single speed sprockets are thicker and require more space between the links. Hub spacing is also different, 110mm for a coaster and 135mm for typical 7-9 speed cassettes, so you will have to add spacers and center/align the wheel yourself. Then you will have to make sure the rear sprocket will align with one of the front sprockets, which will most likely be the smallest. I can't say for sure since I have never tried to turn a geared bike to a single speed. And obviously you have to swap your engine sprocket over to the new wheel and align it properly to. Just make sure you go with a Shimano coaster, they seem to be more consistent when breaking than other brands. I've also seen pictures, here on the forums somewhere of Falcons or Hi Stops that cracked under the extra speed and/or weight of the engine.