1) Do not worry about getting gold medals on your first playthrough of the game. Instead work on unlocking each chapter and "leveling up" your character. This will make your gold medal plays much easier. IMO the best chapter to level up on is 5-Ferry Ride. The level is tracked so you do not have to worry about which way to go. You can easily earn approximately 500 carbon and 300 titanium. Use these to purchase your wicked armor and level up your secondary weapons; which as they level up will also impact your characters performance when not using them. Exp gained can be used to increase the stats of your character.
2) DLC levels DO count towards this achievement, so you can pick and choose which 10 levels of the original you want to do (Completing the 3 dlc levels with gold medals is an achievement).
Of the original levels I found the following to be the easiest:
2-To The Rescue
3-A Daring Escape
9-Belly of the Beast