I like Sentinel, but I prefer it with a weapon bonus talent to increase the DPS.
Typically I would recommend someone start with Soldier if they are brand new to the series, but everyone has their own preference. A couple things to keep in mind though are that the early game weapons aren't particularly good, although some NPCs will give you a semi-decent pistol on Eden Prime which you should equip, and the Pistol and Assault Rifle really need Marksman and Overkill activated respectively to do decent damage. Granted it has been a while since I played Veteran so maybe they work a little better on that level (if I remember correctly, that is the highest level you can start at if you haven't beaten the game once already).