Install full firefox or portable firefox on a new computer?

Well, you're asking if blue is a nice color. It sure is, if you like blue.

That said, there's a few things you should know. Do not install the portableapps to the Program Files directory. Windows is quite protective of it, and will get upset with you.

If you want to use portableapps, you'll generally lose the ability to have default actions work based on file types. So, you'll have trouble making your computer open ThunderbirdPortable when you click on a mailto link in your browser. It can be done, but it takes a lot of effort and manipulation.

So you've got to decide if that's what you want to do. Understand that if you mess with enough stuff to make it work, that you don't have a "standard" portable installation anymore (or a standard computer setup either). You've only succeeded in modifying your computer to do what it would have done had you installed the normal application in the first place. And you lose the easy swap in-and-out features of using portableapps.

Personally, I've come full-circle and carefully chosen a few non-portable applications to install, and then use portable apps for the rest. The actual installs include Firefox, Thunderbird, LibreOffice, and not much else. Updating them isn't going to muck up anything. And the benefits of the installation are worth it.

For Firefox and Thunderbird, you can back up the profile directory and then copy that profile into another install or even a portableapps version you keep on a USB. For LibreOffice, the only backup you really need is the documents you've created.

You'll probably get other advice, too... but decide for yourself what you want to do, and if you like the color blue.

I find it a lot easier to stick with just one Firefox, rather than having two different ones. So I Always use Firefox Portable even if I'm using my own PC.

The advantage I see in installing portable apps on a local system is that you can easily back up (or rescue) apps as they are. I find this especially important in a few instances:
1. I have added my own configuration, or added plugins to the app.
2. The app stores data as a part of its function, such as in a database or encrypted files.

Firefox definitely falls into category 1, and Thunderbird falls into both categories. Other apps that benefit this way include Filezilla, Kompozer, Calibre, Audacity and the GIMP.

I don't install LibreOffice as portable, partly because I don't alter it, and partly because there are still a lot of bugs (in the original), and I'm too impatient to wait for the portable version. Once they work out the PDF export problems, I'll probably switch to the portable version.