I have a squier strat and i've been playing for about a year. I would like some good advice on guitars that are (at absolute most) $700, preferably 500-600. I'm going for a classic rock/blues type of vibe.
Why not a nicer Fender Strat? I've heard god things about the Deluxe Player's Strat and I think it's in your price range.
My Gear:

Washburn WI14 Electric
Washburn D10s Acoustic
Marshall MG100HDFXR Special Edition
Marshall MG412AR Special Edition

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I had a squire strat and from there i got a carlson custom made from the factory. I would suggest a fender strat or maybe an epiphone lp custom, Personally i would take an lp over a strat.
I think that an Ibanez is nice. It doesn't come with the hefty price tag of a Gibson and you can get a nice Ibanez for a very reasonable price. I prefer it without whammy but I got an Ibanez AR100, looks kinda like the Les Paul and the sound quality is great. It was my second guitar as well. Just came off of a strat myself. Nice change.
Yeah, id go with a mid range ibanez. Pretty reasonable for the quality you get. Im eyeing up a 2570E myself.

My second guitar was a Squier... im sure ive done this in the wrong order
God knows I don't want to be an angel

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Ibanez SZ series; as has been said, they're very affordable and worth it for the money.