What would be a good introduction to exercise for someone who doesn't do it?

A_Nihilist
So I ask this because I am not a regular exerciser. I very rarely exercise. However as of late I've noticed that I have put on a little weight and I would like to get on top of it before it gets away from me and I become overweight.

However I did three sets of fifteen sit ups leaving three minute rests between each set. One set of fifteen pushups and seven after that set after a three minute interval. I couldn't finish the pushups because they were hurting my wrists. And then I did one set of fifteen squats.

By the end of this I was pretty worn out. My chest was pounding and I felt sick. I wretched a couple of times but didn't vomit.


TLDR;
So my question is, what home exercise routine would you recommend for someone who hasn't exercised in years?
What would be a good introduction to exercise for someone who doesn't do it?
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