While a Live CD does have limitations, you can mount your windows drive under Linux plus you have a temporary space you can write to. In addition, you can use a thumb drive to save data to. It's a common way of saving your settings on a Live disk. On boot, you just tell the system to load settings from the thumb drive. I do that with a couple of Live distros I use.
With that said, that's fine for testing the waters, I wouldn't do that all the time. Especially since you're trying to gain experience working in Unix. You'd want to be able to customize your environment a bit more and install packages that may not be installed on the Live CD. You can install them via the thumb as well, just storing the libraries on the thumb drive. Another issue that bogs me down is the slowness of the CD based system. It's fine for a quick boot and rummage around but again, I wouldn't use it for more than just that.
As to your last question, removing Windows. If you're not using Windows on the system any more and of course your data's been saved
then yea, I'd just punt the whole system and install one of the available Unix distributions.
The problem is that it's a laptop. In my experience, laptops are pretty unique beasts. It can limit your choices of Unix that you can install. Try the Live CD method first, make sure your laptop works as expected in the environment you're looking at and then you'll be reasonably assured it'll work for you as a programmer. You don't want to spend all your time chasing down drivers and tweaking things to get them working.
As to which Unix? Well there's a wide variety that's available to you. I'm not sure you could install Solaris on a laptop. If it's possible and if you want to try, go for it. A better choice might be FreeBSD. I believe it has some pretty good support for laptops. But there are Live CDs for quite a few distributions. Ubuntu seems to get a lot of thumbs up from people.
And the Mac uses OS X which is a FreeBSD based system but using a Mach kernel and Apple's proprietary user interface.
Carl