I'd say that your best bet is to install Netscape first, and then copy over your mail directory.
If you're using Windows 2000 or higher on both computers, this process can be simplified a bit. Open up Windows Explorer (not to be confused with Internet Explorer), and type in "%APPDATA%", without the quotes, into the address bar. You'll get a list of folders -- open the one labeled "Mozilla", followed by "Profiles". Next, double-click on your Netscape profile name (usually "default", though it can be changed). There is a single folder inside this folder, so open this one folder. The resulting folder contains another folder called "Mail". Either copy this to a CD or some other media (a floppy will most likely not be able to fit all of it), or set it up as a network share.
Next, on the new computer with Thunderbird, run Thunderbird so that it will create a profile (if you haven't done so already). The first time you run it, Thunderbird will create a profile. In a similar process, open Windows Explorer and type "%APPDATA%" in the address bar. This time, go into the directory labeled "Thunderbird", then your profile name (usually "default"), then the single folder within that one. Now, just paste your old Mail directory in here. Open Thunderbird, and you should be able to see all of your Netscape mail.
Note that if you had a Netscape WebMail account, you will be able to see your old mail, but you will not be able to download new mail. The problem behind this is that Thunderbird cannot properly communicate with Netscape's mail servers.
UserAgent: Mozilla/5.0 (Windows; U; Windows NT 5.0; en-US; rv:1.0.2) Gecko/20030208 Netscape/7.02
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