As pointed out in other answers, Jim's main objective when he is free is to get back his wife and children, one way or the other. He says he'll steal his children if he has to.  He often talks about his family to Huck, warmly and lovingly. He is a good family man.

Jim expounds on his plans to get back his wife and children quite freely to Huck, not realizing that Huck is secretly alarmed to hear him go on in this way: 'It 'most froze me to hear such talk.' This situation engenders a deep conflict inside Huck, who instinctively sympathizes with Jim; yet society has taught him that it is wrong for a slave to try and escape and, even more, to 'steal' other people's slaves. Huck agonizes over this conflict; he says he almost 'died of miserableness' over it. Of course, the irony is that what society holds to be wrong is right. Slavery is an abominable institution which treats its victims as mere chattels, to be bought and sold. But, in a blinkered little town like St Petersburg, where Huck grows up, no-one questions it.

Huck wrestles with the false conscience implanted in him by society, but he never fails to help Jim, even when he thinks that his actions in doing so will send him to St Petersburg's 'hell'. No matter how conflicted he may be, when it comes to the crunch he obeys the promptings of his own good heart and rejects the false teachings of society. 

...and that is why Huck is battling this great internal conflict. In a society that has taught him that slaves are property, he already views helping Jim as stealing from Miss Watson. Then, to sit and listen to Jim talk about buying his wife and stealing his children makes it almost unbearable to Huck. He feels that he would then be stealing from someone he's never met who's never done him any harm. That's why this decision was so tough for him, and why he's reconciled himself to the fact that he's probably going to hell as a result of helping Jim.

What Jim wants most of all after he is free is to buy back his wife and children. He will do so when he reaches Cairo, Illinois, a free state, where he can pursue their freedom in relative safety.