+1 on the proper stands - don’t bother with anything else until you get those sound anchors. Think of it as a component upgrade, because the difference between having them on the stands and on the floor is at least one component difference. Dialing them in properly is another component upgrade.
On the integrated front, I had a pair of 2CE Sigs with a SimAudio I-5080 (similar to the I-3 which replaced it). It’s very fast, clean, but cool. Holographic soundstage with the Vandys, but again, not at all warm. In your budget, how about a used Rogue Cronus? The other integrated amp I liked with the Vandys that is now long out of business and hard to find - Magnum Audio IA 170 SE. Spectacular, warm, detailed, rare, hard to find now. If you can find one, it would be well under your budget. They were like $650 new.
On the integrated front, I had a pair of 2CE Sigs with a SimAudio I-5080 (similar to the I-3 which replaced it). It’s very fast, clean, but cool. Holographic soundstage with the Vandys, but again, not at all warm. In your budget, how about a used Rogue Cronus? The other integrated amp I liked with the Vandys that is now long out of business and hard to find - Magnum Audio IA 170 SE. Spectacular, warm, detailed, rare, hard to find now. If you can find one, it would be well under your budget. They were like $650 new.