Although you'll spend nearly twice the money to get into a set of Elixer strings, it's money well spent. I know that as a college student I had always heard of Elixir strings but could never justify spending the extra money. However, after trying a set, I have been playing nothing but Elixers for the past 10 years.
I'm not going to pretend to know the science behind any of this, but can tell you that these strings make any guitar sound much better. They typically give a bright, even, and deep tone that you simply don't get with the budget brands. Additionally, they last nearly twice as long before needing to be replaced. Lastly, I will say that the webbing on these strings makes them much easier on the fingers for beginning and experienced guitar players alike. Sliding up and down the strings wont cut you up nearly as bad as other brands.
One point of clarification here: buy the NANOWEB instead of the POLYWEB. As the Poly coating wears off it can be uncomfortable to play and adds an ugliness to your guitar that any civilized being shouldn't want. Keep your baby looking good and she'll be good to you. However, if I remember correctly, the poly-coated strings did hold their sound and playability even longer than the Nanoweb coating, so if that's more of a priority for you don't feel bad about getting those.
In summary, if you're looking for the best guitar strings on the market, you've found them. Figure out the correct weight of strings for your guitar and order some. I highly doubt you'll regret it.