the movement in touhou is 8-way digital rather than actually analogue, so a stick isn't going to offer any more precise control than a d-pad or keyboard. it all comes down to what's easiest for you personally to use. I only really find d-pad playable; one of my friends used to use analogue stick and then later changed to d-pad and another friend only uses keyboard
and yeah, these games are supposed to be hard if you're not coming in as an arcade shmup fan. a suggestion I have for all newer players to seriously consider is try playing on easy mode. I know that in most games easy mode can lessen fun by removing challenge, but with touhou it's often still challenging in and of itself, especially if you're not used to games like this yet, and the difficultly names are tuned for experienced players (most of the later games say this outright, with normal saying it's "for people used to these kinds of games" or something along those lines). honestly, even though I've been playing for years and have a few games I only play on hard/lunatic anymore, there's still a couple games I'll preferentially play on easy because there's still just enough challenge to keep me focused
(I know eosd doesn't let you get to stage 6 on easy.... but there's still 12 other standard-style windows touhou games)
edit: I forgot to say, seconding that 'practice makes perfect' here. if you're enjoying the games, you'll get better at them. when I started I didn't think I'd ever get to the point I'd ever want to regularly play normal or to even touch hard mode in any of them, but I had a good time with them long enough that eventually it just seemed natural