Which component (Phonostage, preamp or amp) in general, would:
Doesn’t work that way. There’s no correlation between these components and the "most noticeable tube effect/experience". In fact, the better the tube component the less it makes you even think its a "tube effect/experience".
Think of it this way. Would you say, "I want the most noticeable transistor effect/experience"? And then, "Will I get that from a phono stage, preamp or amp"? Or how about, "I want the most noticeable digital effect/experience" should I buy a DAC, or streamer? Crazy questions!
Since you swap speakers, and considering what speakers you have, I would avoid a tube amp. Not that a tube amp wouldn’t sound better, but there’d be problems driving some of your speakers. Problems you won’t have with a preamp or phono stage.
Advantages of tubes are of course they sound better. Assuming you buy on the basis of sound quality and not "most noticeable tube effect/experience". If you buy something deliberately trying to add some coloration all bets are off. But if you go looking for the best you can find (in your budget) then it will, almost by definition, be an improvement over solid state. Keep this in mind in case of the odd chance you get something worse.
So you would try a phono stage or preamp. In terms of matching, you don’t mention your cartridge which is the one thing you need to know. Because if you have MM its easy, but if you have MC then you need to know output. Lower the output the harder it becomes to find a good match. The rap on tube phono stages is noise. Not a problem with a good medium or high output MC, but might drive you crazy if yours is .2mV or something like that.
Put it all together, the preamp is the safest bet of your three options.
But that’s just the logical choice. You find any of them strikes your fancy, go for it.