Despite some references and the occasional crossover each series and movie is mostly self contained. So long as you know when each series or movie takes place chronologically you'll usually be fine if you just want to watch one at a time.
The Original Series & Animated Series
The Next Generation (Watch DS9 1x01 Emissary before TNG 6x16 Birthright)
Deep Space 9 (Watch Movie 7 before season 4)