How long before you feel the effects of exercise? How can you track it?

Anonymous
I am very out of shape.
I've never really been in shape.
I'm from the countryside and when I was a kid I was always a loner, I lived in my room because there was fuck all else to do and no interesting people in my town.
Even as I got older my friends weren't of the sporty variety and my job has been desk based so yeah...

But there things stop being so absolutely typical for me. You see, I'm not fat. I guess the term is "Skinny fat". In the past few years I have developed a little bit of a gut but am of a healthy bmi and look not as out of shape as I actually am.

Following my recent breakup and my desire to someday once again have sex with a somewhat attractive girl, and the coming of warm weather again, I have decided I really need to try and get in shape once again.

Gyms are a no-go for me. I live in a countryside that would rival the one where I grew up (damn job...gotta fix that someday soon too...).
Diet isn't really something I have control over either. Limited shops around here, no cooking skills, limited funds, and I have to eat whatever the work canteen serves up.
Plus I think my average daily calorie count is pretty decent.
beer included. I'm not a big drinker.

Today I decided to try and go jogging but... damn I suck. Even though I did it under cover of darkness so the sun and allergies weren't there to attack me.
I could barely go a minute before my heart started beating like crazy and I felt myself getting hot.

So...I wonder...anyone else ever been in a simialr position? Out of shape but not fat and trying to fix it?

How long should I expect it to take before I can start to notice some improvment from my attempts at jogging?
I'm not expecting to be David Beckham overnight or whoever the hot guy is for kids these days but it would be nice to get some physical improvment in my exercising ability and ultimately my shape.
Any idea how to track this?
Updates
+1 y
Why all the mention of weights?
I don't want to put on muscle, I just want to look good and slim. Weights are good for weight loss too?
I don't have any weights though. And I'm probably moving country in a few months so don't want to buy any.
How long before you feel the effects of exercise? How can you track it?
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