As mentioned, Takumar is a 'legacy' name for Pentax-made lenses. It's the same tradition as Olympus lenses being named Zuiko, or Minoltas being named Rokkor. Of the lenses you're interested in, I have the
Takumar-A 70-200/4, which is a rather good manual zoom, and the
SMC Pentax-FA 100-300/4.7-5.8, which is highly underrated. (The 'A' designation on a Pentax/Takumar lens means the camera can control the aperture. An 'F' or 'FA' or 'DA' label indicates autofocus.)
There are two FA 100-300's, and you've picked the good one.
AVOID THE 4.5-5.6 VERSION!! Both the Tak-A 70-200 and the FA 100-300 are keepers for me, but in different realms. I underpaid (US$9) for the Tak and overpaid (US$120) for the FA. Both deliver good images; I happen to prefer the results of the FA. Of course, they're rather different functionally -- the Tak is 'faster' (wider aperture) but a bit slower to use, and the FA looks cheezy but works fast and clean. Depending on your openness to LBA, it's good to have both.
Comparisons: I use the Tak-A (660g) when I don't want to carry the weight of the
Vivitar Series 1 Version 1 70-210/3.5 (880g). And I use the FA (380g) when I don't want to carry the weight of the
Lil'Bigma,
Sigma APO DGL 170-500/5-6.3 (1270g). Yes, weight is sometimes a consideration.