I'll tell you what NOT to do is have a closed mind when it comes to stuff outside of TOS.
TNG, DS9, VOY, and ENT all take a couple of seasons to get good with a few outstanding to ok episodes in the first couple of seasons for the most part. Swearing off them because they might not have Kirk and Spock or an Enterprise would be a mistake since this franchise is so huge.
TOS isn't perfect either despite what purists would have you believe (I guess they don't remember the third season with such episodes as 'And the Children Shall Lead' and 'Spock's Brain') not every episode is 'Balance of Terror' and 'City on the Edge of Forever'.
Even the much maligned VOY and ENT have their moments and it's ironic that ENT is the only show still intact in the new timeline.
Any tips to get me into TNG and DS9? I wanna enjoy DS9 in particular as I've heard as a continuing series, its the best Star Trek has to offer.
For TNG watch 'The Measure of a Man', 'Q Who', and the Best of Both Worlds two parter, 'The Inner Light' is also an excellent character piece.
For DS9 it's harder since that show builds on it's characters so when the good stuff happens it's much more meaningful. Some great episodes without too many spoilers are 'Duet', 'The Jem'Hadar', 'Improbable Cause', 'The Die is Cast' and 'The Visitor' (DS9's Inner Light). That should get you started with DS9, skip 'Move Along Home' until you have watched the whole series.