A shocking amount of good information here, usually this sort of thread is filled with people touting their own preferences as the "best" option.
A few things to bare in mind as you do the insanity run:
1. Start over with an imported ME1 save, not an imported ME2 save. People have already explained why.
2. Vanguard's charge can save you from having to fight additional waves at some points, but be aware that the Vanguard is a generally ill-equipped class for playing Insanity.
3. Regardless of what anyone else says (and people will try to tell you that their favourite class is "best") Soldier is the class best for playing Insanity. It has the highest damage output with the Mattock/Adrenaline Rush combo. Adrenaline Rush will also save your ass, and the ammo powers fit any situation. It is, unfortunately, a boring class to play and the Mattock is DLC.
4. Check some form of guide or walkthrough to see what kind of enemies you'll be up against, and take squad members who specialise in damaging the enemy's defenses. Don't forget to check what weapons you're using, too. The Geth shotgun, for example, is a great weapon, but not against Husks. To re-use the same example, the Mattock assault rifle has the best DPS, but it's semi automatic and also not suitable for use against Husks.
5. Unlike other difficulty modes and the entirety of ME1, you'll need to use squad commands. There are several moments (usually the moments with Praetorians) when you really need to have team mates take the heat off you by having them attack a particular enemy from a specific location.
6. For loyalty powers, take Barrier. Barrier is the only shield based loyalty power that's affected by upgrades and it has no activation animation, meaning it just springs up instantly, even if Shepard is downed or staggering from a flamethrower/missile hit. It will save your life.