Really, it doesn't make a huge difference, as long as each series is in order, because there is very little overlap, but if going in sequential order is really important, this is the order you can go (its not exact - if you want it perfect, check the Memory Alpha timeline).
- Enterprise, seasons 1-4
- Star Trek, seasons 1-3
- Animated Adventures, season 1-2
- Star Trek films 1-6
- The Next Generation, season 1-5
(now it gets complicated...)
- Next Generation, seasons 6-7 & Deep Space 9, seasons 1-2 - alternating episodes between series
- (film) Generations
- Voyager seasons 1-3 & DS9 seasons 3-5, alternating
- (film) First Contact
- Voyager seasons 4 and DS9 season 6 alternating
- (film) Insurrection
- Voyager season 5 and DS9 season 7 alternating
- Voyager, season 6-7
- (film) Nemesis
- (film) Star Trek
It's not a perfect order, but you'll get the basics.
Honestly, if you just watch each series in its own order, you'll get 99% of what's going on. You may also want to watch Enterprise after Voyager - even though it takes place earlier, a lot of stuff is a subtle reference to other stuff, because it was a prequel.