What strength exercises should I start with?

This is a good beginner routine to work with.

http://startingstrength.wikia.com/wiki/The_Starting_Strength_Novice/Beginner_Programs#Practical_Programming_Novice_Program:

Steer clear of machines (you don't need them).

Keep it simple, and give yourself rest days.

Don't worry about isolation exercises, people that do curls non stop are just....well they are just there as poor examples.

I also recommend reading over this:

http://4chanfit.wikia.com/wiki/Harsh's_Worksheet_(WIP)

Yes, it's from 4chan, a weird, terrible corner of the internet. However there are a bunch of really smart people into fitness and nutrition on there. That page will be a bit crass, weird, and all those other things but it has one of the most detailed run downs on health/fitness/nutrition I have ever seen.

The big ones. Compound exercises (meaning uses two or more muscle groups or joints). Squats, dead lifts, chest press, lat pulldowns, rows and military press. Learn proper form and start light until you are ready to increase. Once you get these figured out you can start adding in isolation exercises that compliment the big lifts.

Press-ups, sit-ups, squats. The most basic, you can do anywhere any time, for free. You only need yourself.

Try working through the Hundred Push Up Challenge, the Two Hundred Sit Up Challenge, and Two Hundred Squats Challenge. Build your base strength before you commit to a gym or anything.

http://hundredpushups.com/
http://www.twohundredsitups.com/
http://www.twohundredsquats.com/

Once you have a strong base to work from, from completing these exercises, then you will have better strength and it will help keep your form to do more targetted work-outs.

My personal experience doing much the same as you with mostly cardio and jogging - I was about the same weight as you with little upper body strength - press-ups and sit-ups and squats really will do wonders.

Strong Lifts 5x5. It's a free program made up of squats, bench, rows, shoulder press, and deadlifts. You start with low weight so you can learn form then progressively move up weight. It's great for establishing a nice solid base of strength.

Thanks guys! Will read all of them right away. I have another question, should we do strength exercises right after cardio or today cardio tomorrow strength? I heard/read that it will help us to burn more if we do strength after cardio. Is this true?

Do strength, then about 20-30 minutes of moderate to intense cardio (don't go for broke).

personally, I'd say to ditch the cardio entirely for now unless you are preparing for an athletic event. If fat loss is your goal, focus on your muscle building efforts and forget the hamster wheeling.