I think if I were a new comer to the show I would absolutely hate TOS. I still find the majority of those episodes to be crap even though I grew up watching them. I could see an episode like "Spock's Brain" where the gogo chick aliens steal his brain and McCoy is controling his via remote control being a huge turn off to modern viewers.

If you end of finding you have a hard time sitting through them, I would recommend just skipping through it onto the films, or watching some of the better loved episodes and skipping over the majority, then you could always go back and watch them later. Just a thought. The series really gets at its best during the TNG DS9 era. It would really be a shame for you to grow tired of the show while working your way through TOS and TAS and never make it to the parts of the series that are really worthwhile.

Good choice on not beginning with Enterprise by the way, it really doesn't have that Star Trekkish feel of the others, in fact the first season was officially just titled "Enterprise" it wasn't until season two that they decided to add the "Star Trek" above the title.