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Hard to answer as everyone's needs are different. But for a guideline I give you my own budget I had for Sofia to start with.
A furnished city center apartment of 60 sq (1 b/r) with everything in it, cleaning lady once a week, living expenses some 150 lv a week, going out twice a week, no need for big food shopping as I am single but more for beer, LOL I come to about 1900 lv a month.
No, this is by no means posh restaurants but where locals would go, no expensive drinks or spirits just BG stuff and when going anywhere taking the bus as no car. Hell, don't need a car in Sofia.
But life is pretty good, I am not short of anything, utility bills are already included in above just add long distance holidays or major purchases like a new iPad or notebook.
OK, many can live with much less and some need more, just depends.
For wife and kid, well, probably you need a little more.
Now, it is fair to say that I earn far more then 2k lv but that is the budget I set myself early on and could manage pretty well on this.

All the best!

PS when my son came to stay he blew my budget easily but then he eats for 3 and drinks like a fish!...LOL