You might also want to look into the Paul Reed Smith 'SE' line of guitars. These are the Korean-made versions of the high-end PRS guitars made in the states. Some of the more basic ones can come in used at around $300.00, give or take, and are very nice guitars for the money. Even the ones with gorgeous flame/quilt, nice inlays, etc., can be had cheap! Some examples from Reverb:
https://reverb.com/item/3558027-prs-...lectric-guitar
https://reverb.com/item/3748933-paul...m-22-flame-top
https://reverb.com/item/3627109-prs-...-2008-sunburst
Like most Gibsons, they have a slightly shorter scale length (the distance between the bridge and the nut) and neck dimensions that are very hand-friendly for starting out, and their build quality, tone and playability are stellar. I wish there were guitars this nice for little cash when I was starting!
I think I would be hesitant to start out on a guitar with a floating type tremolo, especially in this price range...they're hard enough for experienced players to get and keep in tune. I think I would start with a hard-tail or possibly a basic trem that's set for "dive-only". You want to be able to learn how it's supposed to sound when it's tuned right. Just my two bits...
Enjoy the journey!