No, you don't need a hardening fixer for TMax films. The only film (brand) that I know of where a hardening fixer is recommended is Efke film (which is also known as Adox CHS and maybe some other names).
Last night I order some TF4 from the Formulary, I was going to order it from Freestyle but they didn't have the quantity I needed and the Formulary is closer anyway. I have been using TF4 for a year or two now and really like it. I bought several gallons of distilled water for the new batch.
TF-4 would be a good choice. It works quickly and well, and it washes out easily. Unless you have serious water problems, you don't need distilled water to mix it - tap water works fine. Modern films like TMax don't need hardener, but some older style films made in eastern Europe (and some specialty films) may benefit from it. Fixers with hardener usually require more wash time than fixers like TF-4.