Definitely play TA from the get go, its by far the better game. They do good bundle deals so you can "catch up" re versions of the game. Once you get all three, you'll get all the updates for all of them, so whatever Campaign you decide to play, it'll be updated with that Version.
The Campaigns are not "free standing", they only run within the Version environment that originally created them. Game enhancements/bug fixes are - as such - not "backwards compatible", and only apply to the Version for which they were created. Some can have a knock on effect, for example you must have DA loaded to run TA, so some DA fixes can have a knock on effect.
However, bottom line, dont worry about it, you'll be fine, the update process is very good. Just let the Stardock automatic update process do its thing and all is well.
Regards
Zy