If it helps, not trying to be flip, I didn't want to go past $900.00.
My journey started with learning how to dial our pre-existing subwoofer system in. Then it became about getting the best out of what we had as I replaced drivers/radiators and purchased an additional outboard EQ system (Anti-Mode 8033S II) to compliment the existing Audyssey MultEQ XT that was included with the recently upgraded AVR. Continuing, we (I) added a third subwoofer and for the first time, subwoofer wise, the room came alive. At this point, I've put six months and a thousand dollars into this journey. For education purposes, I consider this money well spent.
After going through the above, I realized, to get where I wanted to go, I would have to go to the "Dark Side" and jump in and get all dirty, throwing any rational budget to the wind. From my above experience, it was patently clear, to get to where I wanted to go, it wasn't going happen on a nine hundred dollar budget.
Well, here we are, you asking about a thousand dollar budget and me waiting for $2,600.00 worth of subwoofers to arrive and I, keeping my options open to adding a third subwoofer to the mix. Based on all I've learned, trying to stay close to your stated budget, I would recommend starting your journey with a pair of Rythmik LV12Rs, download a freeware copy of REW, learn how to get the best out of these two subwoofers and keep your options open to a third or fourth LV12R.
In my opinion, based on personal experience, that would be the most rational approach. Later, when you realize that the "Dark Side" is where you really want to go, then you'll better understand why I post what I posted above.
Hope my above helps clarify my comments.