Although I haven’t used one, I’ve had a couple of Schiit DACs and would not hesitate to use their other kit, too.
Cheapest headphone amp is, I think, the Magni 3+ at about £125. My brother has recently said he wanted to try a headphone setup and I will suggest he goes for the Schiit and I won’t spend any more time thinking about his alternatives. I’ll just tell him to go for the Magni.
what I don’t know, though, is whether your Linn pre-amp has any special requirements (e.g. balanced connections, etc).