Don’t worry about vertical speed, concentrate on air speed. The faster your air speed the slower your climb in the Airbus. . For climbing above 10,000 ft I use selected speed of about 273 which will get you about 2500 ft per minute which will gradually reduce to about 800 ft per minute at about 30,000 depending on weight and fuel. The managed control speed of 320 above 10,000 is way too fast. So for me, flying at managed speed up to 10,000 and then 270ish selected above gets me a nice easy climb. On decent I use about 250 selected all the down to 10000 ft then managed under that though I sometimes keep it at 240 selected if I think dec is going to slow me down too much and I have a longer distance to airport. Anyway that’s how I do it and she flys like a kitten. This is the default A320 I’m talking about. I use to be a Boeing fan but I’m in the Airbus camp now.
Edit: keep in mind that 270 true air speed is faster at 30,000 ft than at 10,000 ft hence the slower climb rate at 30000. I use managed speed at cruise. I know when it’s time to descend because my engines will spool down when descent comes on my MCDU. I’m not a pro here at all but just do what I feel works.