I really like my little hub gear bike, and I'm currently upgrading my full-size derailleur bike to a hub gear as well, but I agree with the other comments that what you really need is some adjustments to your cables and/or your derailleur settings. Also, there's other places to look for clicks, but given that you aren't always shifting when you want and the chain sometimes hits the front derailleur, it seems likely that at least some of your problems are related to derailleur function. If you're not comfortable messing with that yourself, take it somewhere for a complete tune up asking them to pay particular attention to the shifting and the drivetrain.

I would never discourage you from getting an internally geared hub, but the problems you describe should be fixable for considerably less then the expense of an IGH system. Also some things to consider if you do go with an IGH:
If you go with anything less than a Rohloff you will probably lose some of the range you currently have unless you continue to use a front derailleur. Many people find that the gear range of your typical 8 or 9 speed hub is all they need, so it might not be an issue, but it also probably won't be as large of a range as you are used to.
An IGH will move your chain farther out from the center in the back, meaning that you'll probably need to move it farther out in the front for proper chain line. I believe this usually involves replacing the bottom bracket.
Your front chainrings may not be an optimal size for your new hub, so those may need to be replaced, too, but you can probably get by with two, rather than three (or one, if all of your shifting is going to take place at the IGH).

In short, just about every part of your drivetrain will possibly need to be replaced. Not that it's not worth it, but it's something you should take into consideration going in.