I have owned a few Bursons and I currently own a Timekeeper 3i that I use as one of my headphone sources and to power a near field speaker setup. You can’t go wrong with Burson products. They’re very well designed, they sound great, and the customer service that comes with them is second to none.
I own the Tk3i because it suits a very specific use case for me. That said, if your use case allows you to use separate amp and DAC components I would recommend you go that direction. Not only does it give you more flexibility in upgrading or changing your rig, it also makes it so that potential failures only effect a single component rather than the entire combo.
With that in mind, I’d say go with the Soloist 3XP and the DAC of your choice. Before I recommend possible DAC choices can you tell me/us what you’re looking for in a DAC both as far as potentiak sound signature goes as well as any features? Also, do you have a preference for a particular DAC chipmaker you’d prefer or R2R? And last, but not least, what is the budget for this DAC that you’re pairing with the Soloist?
If you’re looking to add some body and also good values on the used market, if you can find a good deal on a bryston bha1 that’s absolutely worth a look. The soloist 3xp will be nice, but imo an amp more on the dry side of things, and I wouldn’t really consider it all that spacious. But it is a good amp for the price for the hek, and also nice flexiblity on the dac pairing side of things, whereas if you went bryston (or the aforementioned violectric at least older series like 281) you’d have a bit less dac flexibility, but in exchange I’d personally put the bha1 or 281 over burson stuff for what you look for
Another solid option in the range is the gsx mini, which while I do think would have nice body and openness with the pairup, it is somewhat tighter and more compact in the stage imo. This can be corrected with the right dac pairing, but it’s still not going to be a very wide sounding amp, but does have great placement accuracy and depth, moreso than the burson still. Actually starting to come down to decent value prices in the used market so worth a look
I am not a fan of AIO, but they are good space savers, and in theory they are tuned to work well together. I would suggest going with a stack. It eliminates a single point of failure, and it allows you to mix and match later on if you want to change things up down the road. Everything in the signal chain affects the end result for better or for worst.