Here's my suggestions. If I made a comment, then it means you should probably see it. There is an ongoing sequence of events with the Andorians, Klingons, and Vulcans so any episode centered around them should be watched.
First season:
Broken Bow -- not a great episode by any means, but any first episode should be seen.
Fight or Flight -- skip it.
Strange new world -- skip it.
Unexpected -- never saw it so I don't know.
Terra Nova -- skip it.
Andorian incident -- a must see, as there is a continuing Andorian storyline.
Breaking the ice -- skip it.
Civilization -- skip it.
Fortunate Son -- skip it.
Cold Front -- sets the whole future temporal war thing.
Silent Enemy -- has some good character development so maybe worth watching.
Dear Doctor -- good episode showcasing Billingsley's (Phlox) incredible acting skills.
Sleeping Dogs -- First time aboard a Klingon ship, sets tone for future Klingon aggression.
Shadows of P'Jem -- Andorian episode, good one. Sets tone for increased Vulcan-Earth tension.
Shuttlepod One -- skip it.
Fusion -- an OK episode if you want to see what Vulcans were like pre-Spock days.
Rogue Planet -- skip it.
Acquisition -- Ferengi episode. Yes, they aren't supposed to be known about until the 24th century but the episode covers that twist.
Oasis -- Odo episode, well OK, not Odo but Rene Aubujornois (sp?) is in it. He was supposed to be in more episodes but it never happened, don't know why.
Detained -- Suliban episode, future episodes make reference to this episode so you should watch it.
Vox Sola -- skip it.
Fallen hero -- vulcan episode, not that great, not important.
Desert Crossing -- Good episode, incredible character development between Archer and Trip.
Two days & two nights -- skip it.
Shockwave -- Season finale, always worth watching these.
Season 2:
Shockwave II -- season opener, watch it.
Carbon Creek -- meant as comedy relief, not a serious episode.
Minefield -- Good solid episode introducing us to Romulans
Dead Stop -- Another good episode, Borg?
Night in Sickbay -- skip it.
Marauders -- Good episode, klingon hostilities.
Seventh -- Not bad, action packaged episode!
Communicator -- skip it.
Singularity -- skip it.
Vanishing point -- skip it.
Precious Cargo -- skip it.
Catwalk -- pretty good episode from what I can remember.
Dawn -- Skip it.
Stigma -- another Vulcan diplomacy episode, very slow moving episode but I guess you'll need to watch it to understand the whole vulcan issue.
Cease Fire -- another Andorian episode.
Future Tense -- Great episode, freaky encounter with Tholians.
Canamar -- Another rare good one.
Crossing -- skip it.
Judgment -- Klingon episode, one of the best episodes.
Horizon -- Good episode as it shows life aboard a cargo ship.
Breach -- skip it.
Cogenitor -- skip it.
Regeneration -- Borg episode.
First Flight -- good episode only because it goes into the past, during the test days of Enterprise.
Bounty -- another Klingon episode.
Expanse -- season ender.