Are clip-on shoes necessary?

I'd say go for it. Last year I was in the same boat you're in, and eventually decided to go for it. After getting used to them (and falling a few times!), I fell in love with being clipped in. I wouldn't go back. The increase in power was very noticeable to me.

Also of note is how more efficient you become with your pedal stroke. With clip-on shoes you learn to use both legs on both pedals the entire pedal stroke. I highly recommend them.

Thanks everyone!
Are there any brands you recommend? Preferably on the cheaper end of the scale.

I often buy Nashbar stuff for cycling when I want something that isn't fancy (read - not too $$$) but will do the job and last a while. Their gear is relatively inexpensive but I've had very good luck with it and has lasted well for me. I have had a pair of their mountain bike shoes that lasted 3 years of moderate use and are still in my closet and look fine. 'Had a pair of their MTB SPD pedals that lasted two different bikes. I have their chromatic sunglasses for 2 years and they gave me free replacement lenses when I accidentally scratched them (my fault) and I wear them daily. I've got a pair of their cycling shorts that are very nicely built and have great comfort. I've also got one of their pump/inflators, minitools, bike computers, and various other things... Overall, I've been very pleased and they dont hurt my wallet much.

I do own a pair of their road shoes and like them very well and would recommend them for a lower budget recreational rider. Normally $49 and you will often find discount codes. http://www.nashbar.com/bikes/Product_10053_10052_550746_-1___

For pedals, the Shimano R540's for $30. http://www.nashbar.com/bikes/Product_10053_10052_527070_-1___204720

Not a bad combination for a $80 budget, maybe less with some codes.