It might help to realise that 好き is an adjective.
Thus, 'music I like' is as easy as 好きな音楽 - 'liked music', to translate it very directly. For 'Touhou music I like', 好きな東方音楽 would do just fine.
If you're not also creating a playlist for music someone else likes, then you can leave 私 out entirely.
As for 東方の音楽が好きだ私, you might benefit from a breakdown of the issues with it:
As it stands, this is a full sentence. It sounds like 私 is a very backgrounded topic, something like how some UK English dialects might say 'I like Touhou music, I do'.
If you want to put 好き in front of something, you're probably intending to modify it. To do this, you have to change 好きだ to 好きな, using the relative clause forming form (rentaikei) of だ.
Unfortunately, this change (to 東方の音楽が好きな私) makes it a noun phrase where the head is 'me' - it comes out sounding like 'me, who likes Touhou music'. You'd need to put 音楽 where 私 is now.
This leaves you with 私が好きな東方の音楽. Because 好き doesn't line up quite right with the English word 'like', this comes out as 'the Touhou music that likes me'. Xが好きなY is 'the Y that likes X' - to make it 'the Y that X likes', you need the が to be は or に, and since は isn't permitted in subordinate clauses like this one, you need に. (Overall, 好き works like this: LIKERは/に LIKEDが 好き)
This gives you 私に好きな東方の音楽, which is decently serviceable. As I mentioned above, you don't really need 私に if you don't plan to contrast this with playlists of Touhou music that other people like. And as for 東方の音楽 vs. 東方音楽, I might be wrong here, but 東方の音楽 sounds like 'music from Touhou' (i.e. Touhou is a specific work) while 東方音楽 sounds like 'Touhou music' (i.e. Touhou music is a category of music). So to me, without further context, the most naturalistic translation is 好きな東方音楽.