Welcome to the forum.
The most common advise you'll get here will be:
Go to a range where you can rent some guns, and shoot a whole bunch of them to figure out what you like, and shoot, the best.
In your price range, you should seriously consider looking at used guns. You can't get a heck of a lot in a new firearm from a major manufacturer for under $350 except for stuff like Hi-Point or Rossi, which is famous for being junk. (not to insult anyone that carries one, though...)
You said you wanted something lightweight, and effective (which I assume means "of a good man-stopper caliber").
With that criteria, I'd check out a used Springfield XD, Glock, or other polymer-framed pistol in 9mm.
I personally prefer a larger caliber (*cough*.45ACP*cough*) but practice is incredably important, and if you're already on a tight budget, you should pick a caliber you can AFFORD to practice with.
9mm, with good hollowpoints (such as Federal's HST or Speer's Gold Dot) is an acceptable manstopper around, and practice ammo can be had very inexpensively.
But again, I stress: Go shoot some guns and see what you like, and what you can shoot well with. In your price range, look at used guns. Shoot it before you buy it.
Just my inflation-adjusted two cents.
After I made this post, I googled a bit, and sure enough, you can get some decent guns brand new around $350:
S&W model 910
A little closer to $400:
Any of those would probably meet your criteria. I'd seriously consider that Ruger SR9.