He sounds exceedingly impractical, and you're right in getting annoyed and angry with his lack of intention of sorting his life out. Do you really want such a man as your future husband? Someone who would be in financial mess, refuses to pull himself together AND argues with you a lot? Yes, you don't break up over stupid arguments, but a relationship with numerous arguments all the time is an unhealthy relationship and you need to start identifying just why you're arguing so often. Are there any other underlying issues other than money? Any personality clashes, clashes in how you view things? This clash in attitude to life and to money, specifically, is a serious problem and unless you two can agree on this you're looking for a lifetime of arguments with him. I say you should consider breaking up with this guy. Such a man cannot support himself, let alone a family, and do you really want such a man to be the role model for your children, to be your children's father-figure? Marriage is nice and romantic and it does come with all the pink and fluff and fairy dust, but it is also a practical matter, a realistic matter. Is it realistic to have this man as your husband, given how you argue, given his attitude to money? Is he willing to change in this respect? If not, then you're stuck - you have to break up with him or put up with a lifetime of uncertainty and heated arguments over money-matters, and bear in mind that money is an issue in everyday life. You need money for the rest of your life, which means this attitude towards money will annoy you, if he remains unchanged, and cause damage to your relationship and your children in the future.
We all like to think our current partner is to be our future spouse when it's been a good relationship - but whether or not he really is to be your future spouse is quite different to the fluffy feelings that you feel from time to time at the thought. I still think sometimes that I wanna marry my ex, but the rational side of me knows that he isn't right for me. And when you're in the relationship, the hardest part is accepting that he isn't right for you, if indeed he isn't, and deep down you'll know whether he really is right for you, or if you simply WANT him to be right for you.
And you cannot give him indefinite chances - you know better than anyone whether he'll change. It's like, even a year ago I knew my ex would never leave Germany, but I held onto the hope that he just might, and deep down I knew he wasn't right for me but I held on. But what's the point? Give him one chance - and that's it. Everyone deserves a second chance, yes, but after that chance, it's goodbye. Don't confuse him being right for you with you wanting him to be right for you. However much you might want it, it doesn't make it true.
And "improving" isn't good enough. He needs to change. Yes it will be a gradual change, but in his head it needs to be a change, not an "improvement." Yes there will be setbacks and I'm not saying break up with him if he fails - but you can tell whether the intention to change is actually there. If the intention isn't there, break up. If the intention is there but still he lacks the discipline to push through and actually do it, then break up. You need to be seeing actual improvements, even if they're as slight as him sending off a few application forms instead of none, or wearing a suit to an interview instead of jeans - but improvements nonetheless. You need to tell him - this is it, if you don't change, it's the end of us. You need to make him realise that this is gonna cause him to lose you, and if you're important enough to him, if he thinks that you're meant to be his future wife, he WILL change. But if he doesn't, then you need to end it.