I want to start exercising, which I haven't done in ages (apart from riding my bike to the train station). I was thinking about doing power walking or jump ropes. How often should I exercise every week (let's say for 30 minutes)? What would you suggest?

they usually say 3-4 times i week if i remember correctly.
i should excercise aswell but i am so lazy...ha

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And I want to play hide-and-seek and give you my clothes and tell you I like your shoes and sit on the steps while you take a bath...

It depends on how much time you have available... 3 times a week is good to get fit, as long as you make sure you raise your heartrate to cardiovascular level at least once or twice a week in those sessions.
I work out around 4 times a week because I don't often have time for much more