Personally, I don't see him winding up a serious contender for the nomination. He'll do better than the even more inexperienced and less-disciplined Ben Carson. He'll probably gain a higher share of votes in the early contests than his father did, but Scott Walker and Ted Cruz will probably be the strongest competitors for the most conservative part of the GOP while Jeb Bush commands the establishment. Walker, by virtue of his having executive experience and attempting to position himself as a leader who has demonstrated an ability to make tough choices, even if they are controversial, might have the edge on Cruz. However, Cruz's Super PACs have raised a lot of money early on, so Cruz will have some staying power. Cruz, like Paul, can be undisciplined at times. He can also be polarizing. If Cruz takes on an anti-GOP approach, he'll fade and as he does so, Walker could snap up those voters.
It's very early, so a lot can still happen. However, at this point in time, I am fairly confident though that Ben Carson will be a non-entity on account of his lack of leadership experience and often inflammatory comments. Senator Paul probably won't wind up a strong contender either on account of a combination of his lack of experience and extremely difficult transition needed to gain broad-based appeal. Governor Christie already imploded and stands little chance of regaining his earlier position, especially with Jeb Bush seen as the Establishment candidate and New Jersey's again bumpy finances.