If I was you...I watch the series in this order (yes, TOS is the first series and Enterprise is the 5th series), start with Enterprise first since it takes place 100 years before TOS, then watch TOS after that. After your done with those 2 series, then watch TNG next, DS9 after that and Voyager last.
Just to point out that TOS only had 3 seasons and Enterprise has 4 seasons. You'll get through those 2 series pretty fast before you even know it lol
And don't forget one thing....enjoy!
If you wish to know what years the shows started and ended (and also what years in the trek universe it takes place from start to end going by how long the shows aired)...here:
1. The Original Series (TOS)- Sept 8, 1966 to June 3, 1969 (in Trek Universe, 2265-2269), 3 seasons (79 episodes)
2. The Next Generation (TNG)- Sept 28, 1987 to May 23, 1994 (in Trek universe, 2364-2370), 7 seasons (178 episodes)
3. Deep Space Nine (DS9) - Jan 3, 1993 to June 2, 1999 )in Trek universe, 2369-2375), 7 seasons (176 episodes)
4. Voyager (VOY) - Jan 16, 1995 to May 23, 2001 (in Trek universe, 2371-2377), 7 seasons (172 episodes)
5. Enterprise (ENT), note: it was just called Enterprise for the first season, when season 2 came...they added Star Trek to the title (Star Trek: Enterprise)- Sept 26, 2001 to May 13, 2005 (in Trek universe, 2151 to 2154 "final episode in season 4 took place in 2161"), 4 seasons (98 episodes)
There has been 10 Trek movies.
The first trek movies are the TOS movies...
Star Trek I: The Motion Pictures (2271)
Star Trek II: The Wrath of Khan (2285
Star Trek: III: The Search for Spock (2285)
Star Trek: IV: The Voyage Home (2286)
Star Trek V: The Final Frontier (2287)
Star Trek VI: The Undiscovered Country (2293)
The Next Generation movies are:
Star Trek VII: Generations (2371)
Star Trek VIII: First Contact (2373)
Star Trek IX: Insurrection (2375)
Star Trek X: Nemesis (2379)
Here are some sites you might be interested in looking at the learn about Star Trek more and its trek universe: