I think you should research your situation a bit better cmvidini. Don't get me wrong, we've all been there, but if you need to ask if there is a conversion between ATR and 737, well, that tells me that you don't yet fully understand the field you are playing in.
Having said that, all things being equal, the only risk in paying for the ATR-job is that later on you might have to pay again for a jet type. But at least you have a job. If you pay for a 737 type, you still have to find that job in a very bad market...which is the greater risk for you? You mention the salary difference, but that is totally irrelevant IMHO! Can you really afford letting a firm (??) job offer slip away?
Again, having said that... are you very sure about this 'job offer' through a family connection? One thing that strikes me is: Why should you pay for linetraining if there is a job there for you anyway? Not that it doesn't happen, but it should raise some quesion marks. Also, this world is full of charlatans who will promise you anything. Have you got any guarantees on paper?
Stay sceptical all the way, and please, do some basic (again, no offence) research!