This is such a wide open question that it's hard to know where to start. I think we'll need to know at least a few more pieces of basic information first.
1.) Cost - Are you wanting to spend $500 for everything or 100k for everything? You say you could spend "a lot" - what does that mean? Or better yet, what are you looking to spend as you said you'd like to keep the price commensurate with the speakers.
2.) Do you have a preference towards separates vs integrated?
3.) Do you want to go with solid state, tube amp - or open to anything?
4.) Do you prefer a sound that is highly resolving and detailed - potentially bright, or do you like something that is more laid back - a bit easier to listen to?
To give it a shot in the dark, I'll say that I don't have the X-LS, but I did just build a pair of X-Statik's which use the same drivers - just more of them and some in an open baffle configuration. I have found my tube amp to be sublime with them. My current tube amp is a PrimaLuna Evo 300 integrated amp, which I have paired with an RME ADI-2 FS DAC, and I'm using a Bluesound Node 2i to stream Tidal to the DAC. That front end would cost around 6k - if you're looking to spend less then maybe a Willsenton R8 (never heard it but it has excellent reviews) would be a great choice if you're interesed in tubes - and you could use the DAC in the Bluesound without a separate DAC. That would get you in around 2k.
If you're looking for something solid state and an all around decent option, you could look at the NAD M10 which is an all in one amp/streamer/dac that you could get for around $2500.
Let us know more about what your preferences are and price and we'll be able to dial you in a bit better.