Then I would recommend the Ibanez SA series. They're versatile instruments and suitable for many genres of music, and can play pretty much any genre of rock thanks to its sleek design and pickup configuration. I have a GSA60 (the lower-end range) and it can pretty much do it all. Very versatile design.
I would not recommend the Ibanez RG series or many of the other Ibanez designs (XPT, ICT, VPT, S series) because they're more towards hard rock / heavy metal players in terms of design. Actually many Ibanez guitars appeal to the hard rock / heavy metal crowd, just that the Ibanez SA is designed more conservatively so it can do pretty much all.
Perhaps the SA220 or SA260 would be a good starting point, and they're professional instruments so you could still be using them if you go professional, play gigs, etc. The SA260 costs around $750 I think. The GSA60 is a fine instrument for me (I've used it live) but with low-end Ibanez guitars, the quality is quite inconsistent.