The MF was the last of what are generally refered to as the third generation MiG-21s. Thats the M (most without rearview mirrors) MF(most with rearview mirrors) and the R which is a tactical recon version built from either an M or MF.
They come right before the MiG-21 bis in the Fishbed chronology.
The MiG-21 can be broken down into four distinct generations:
First generation: F-12 and F-13 and all subvariants of them with the exception of the Chengdu J-7 Skybolt who's only real commnality with the with the family is being built off blueprints of the F-13.
Second generation: The PF series, the most common of which was the PFM. This series are significantly bulked up from the F-12 and F-13. The most notable recognition feature is the dorsal spine which is very noticably decreased in width midway between the cockpit and vertical stabilizer.
Third Generation: The M, F and R. Somewhat bulked up from the PFs. Most aircraft of the third generation have two piece canopies with the main section hinged to the side, rather than earlier type canopies that were more one piece and hinged at the forward edge. The dorsal spine is much more consistent in width than those of the PF series.
Fourth Generation: The bis. Generally regarded as the last true MiG-21 variant built by Eastern European hands. Beyond having a slightly wider dorsal spine, its largely indistinguishable from an MF.
There have been a couple of offshoots from the main Fishbed line, the above mentioned Chengdu J-7 Skybolt and J-7P Skybolt II, from China.
There is also the Lancer project, which was a very ambitious joint project between Romanian and Israeli aviation industries to extend the life of Romania's MiG-21 MF fleet. The Mig's were gutted of all their older analog avionics and had them replaced with digital gear. They also got "glass cockpits" with CRT screens to replace many of the old dials and scopes. The most striking change was in armaments, the avionics upgrades made the MFs capable of carrying the "Alamo" air to air missile, usually only seen on MiG-29s and SU-27s.
If you can get your hands on 4Plus publishing's reference book on the MiG-21, you'll really be doing yourself a favour. As that outfit is Czech, they can certainly be viewed as a top authority on such birds as the MiG-21.
Hope that helps.