I personally am no fan of Ibanez guitars- they never really feel comfortable to me and they don't generate tones I like. But some people swear by them, so it's up to your tastes. What I would suggest is NOT getting a beginner pack. No matter if it's Ibanez, Fender, Epiphone, or whoever, you're buying a low end electric and a low end amplifier that comes with cheap picks and a short amp cord. If I were you, I would avert my attention from a package deal (like that) and wander over to the used rack. Find a used mid range guitar (which will cost about the same as the new low end Ibanez or Fender or Epiphone) but will sound and play worlds better. Then go look at used amps, and again, go for mid range. If you can do this all at one shop, and the sales people are remotely cool, you can probably talk them into giving you a break on the whole package.

I know money is important (I'm bound by it too), but go by tone and feel as much as possible. Regardless, if you buy used stuff now, you can get a better amp and guitar for equal to maybe $150 more now, as opposed to trading in the cheap Ibanez and amp in six months when you realize that it just doesn't cut the mustard. You have an acoustic now, so you still have something to play on while you save, and beleive me, it's worth the wait to save the extra money.