First:
If you never did an insanity ME1 playthrough before, import an existing character so you do not have to start from scratch.
The level alignment of the enemy units towards your lvl is nothing compared to your offensive and defensive abilities you import a character. Massively helpful.
Your squad depends on personal taste and what sort of class you choose.
Personal taste beat's it all though.
However the Soldier is one of the easiest Classes you can choose throughout the trilogy, turning combat into boot and shoot.
Adept shines in ME1 and ME3 but can be difficult in ME2 due to the different combat system there.
Vanguard is always risky but just as rewarding in high close up damage output, though you'd probably rush through ME1 with you Spectre Pistol.
Sentinels in ME2 (Tech Armor) and ME3 (depending on your bonus power) are almost invincible.
Infiltrator and Engineers powers will render many foes helpless and Engineer's Sabotage in ME3 makes fighting Cerberus a piece of cake (I am looking at you, Grissom Academy).
In ME1 humanoid enemies likes Mercs will use Immunity heavily on Insanity, so a squad with biotics to counter it (Warp, Lift) will make life easier (Liara and Wrex, for example).
Many CC abilities in ME2 can only be applied on Health, and by then the unit is almost down anyway. But they stagger fortified units, which is helpful. By the numbers Miranda and Grunt/Thane are the easiest squad to bring along, with Reaper IFF being the hardest fight in the entire franchise (next to Clone Battle and Mirror Arena Battle in ME3).
ME3 is straight foward..... everything and everyone can and will Combo, so utilize it and pick whoever you like most. Really doesn't matter.
Kassa Colossus Armor with 2 Medical X mods significantly improve your survivability (dmg reduction) and power output (reduced cooldown timers).
Gearwise for ME2 and 3 (depending on Class), pick what you like. I'd recommend Terminus or Blood Dragon and in ME3 switch that with it's Armax Arena counterpart if available.
Happy Hunting.
TL:DR
You can successfully beat the Trilogy with any Class or any Squad, some are easier then others.