I've tried a few amps at various price points with my An-E LX HEs, and all have been good. They all have been of a similar sort-of ilk:
Audio Note OTO SE (upgraded throughout with AN copper caps etc) - very good
New Audio Frontiers 2A3 PP amplifier - even better. Probably best I've heard. Incredible bass. But had to move on as I wanted to go for something more reliable.
Current: DIY valve pre and First Watt F3 SS power. Not quite as good as the NAF, but better than the OTO, and crucially, much cheaper than either. Probably cost me 1300 for the two pieces, and I'm very happy with the combo.
So as long as you're going for a decent quality PP, SE, or a class A SS like Pass labs or First Watt, I can't see you having any issues.