around how many rpms is perfect to shift gears on a manual car

The car idles at around 800rpms and the rpms jump to maybe 1100-1200 and drop below like 500 which is where it starts to stall and often stalls.

Once I succesfully get into first gear and once the car is in motion with my foot off the clutch pedal, the rpm’s stop jumping and the car drives great. It’s only when I push it in first gear and start taking my foot of the clutch and when the car is starting to gain motion that the rpm’s start to jump up and down. The car idles perfect, no rpm change at all and its quiet. at first i thought it was because I’m a relatively new manual driver so I thought I was just getting used to the car but now I know that its not normal. As you would expect from a 20 year old car it does have little mechanical issues and one of them causes the rpm’s to jump up and now when i put my car into 1st gear and take my foot of the clutch pedal. I absolutely love the car, big fan of the looks and drives great. I bought a 2003 BMW 320ci around 2/3 months ago.

Around how many rpms is perfect to shift gears on a manual car