The package you mentioned as a beginners package and is usually a very cheap guitar not only price wise. Check the body and see if it is not laminated plywood. Either way it is a bottom of the line guitar. That's not to say that you can't learn on it as you say you have. They are made to be corner kickers (when intrest is lost it sits in the corner collecting dust) you or the parent is not out $850.00 american for that American made strat.
With that said I've seen people that can smoke on just about guitar it is there talent not the instrument or effects. Youy asked the question what do we think, should you buy a new guitar? Can you afford one? Do you want one? What is cool to me may not cool for you or your style. Play them all and find one that you like.
I just can't get away from strats or strat type guitars. Of my 14 guitars (current and adding) I have 7 strat types (3 Fenders, 1 Washburn, 1 Series 10, 2 Bootleggers,(I made them) and a 1964 Fender Mustang.