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$675 for that second set with Vintage Zildjian A's isn't terrible, but it isn't great. Depending on what the used market is like in your area, you could get used pro-level cymbals (like vintage Zildjian A's) for less. I bought 14" hi-hats for $115 and a 22" ride for $60, both Zildjian A series, and it didn't take too much waiting, lol.
I'd probably go with the first set for $300 (even though it's a mismatch; hopefully the unbranded bass drum isn't trash).
Edit: This is a great "throne" to my ass: [link]
I've never even see those pedals, let alone played them, lol. But if you want a cheap (but still good) throne, I always recommend what I use, which isn't a drum throne at all - the Seville Classics UltraHD Cushioned Pneumatic Work Stool.
Unless you can find a great sale (and I've seen some steals on new drum sets before, especially on Amazon), I think buying used is probably your best bet, especially with a $1000 budget. Also, you may want to spend a large portion of your budget to buy high quality cymbals from the start. Keep in mind that drums can always have their heads changed and also be tuned, whereas there is very little that can be done to change the sound of a cymbal. In my experience, the most common and affordable "pro" level cymbals are Zildjian A's if you are buying used.
Additionally, everyone here seems to recommend buying the best seat (which is referred to as a "throne" for some damn reason...) that you can afford. Popular choices are Pork Pie and Roc-N-Soc. Personally, I use something that isn't sold as a drum throne - this work stool.
Finally, are you a totally inexperienced drummer? I recommend just a practice pad and pair of sticks to start. It's certainly much cheaper, lol.
I always recommendwhat I use, this Seville stool. It's not marketed as a drum throne and it's a bit taller than standard height, but it's very, very durable.