The first mission is challenging without ship upgrades. Seek out upgrades in your factions space station (Carrack Station for Republic or Vaiken Spaceport for Empire). I'm only familiar with the Republic side. Assuming that space station layout is the same, the spaceship upgrades should be in the north-east quadrant of the station. Also, ship upgrades are located near the ship hangers on most planets including Dromund Kass and Coruscant.
I believe the key danger in the escort mission comes at the very end. After you pass the last capital ship, you'll fight ouf 4-5 waves of small fighters. As they enter your screen, their shots typically do not damage the ship you need to protect. Only once they get in close do they start to really rip apart the escort. The key is to get shots on those ships as soon as possible to kill or cripple them early so they don't greatly damage the escort ship.