What should I consider before buying external monitor for my MBP?
What monitor size/resolution I should consider?


This is entirely up to you.  What makes sense for you?  Determine what features/specifications are important, then your budget, and then start shopping.  This will always be a subjective decision


  how will I Connect my mac to my monitor ? HDMI? Thunderbolt ?


This is less subjective; the question is, what does the monitor support?

Your MacBook will have both mini DisplayPort and HDMI  meaning you can use either cable.  Which one you use is entirely up to you, but my recommendation is 


Go with DisplayPort as HDMI can be very flaky (just search this site for examples)
Use the port that matches your monitor - don't convert the signal.  I am a bit proponent of not converting display signals; converting introduces unreliability.  If you must convert a signal, use an active adapter.