I wish you could just equip one weapon in SP. My favorite class is the Vanguard, and now with the Charge + Nova combination, a shotgun is the only weapon I need. Charge into a group, Nova them, and if there's anyone left, give 'em a shotgun to the face.
^You can't just equip one weapon? Strange I thought you could. Next best thing if you want to minimise the weight it so just equip a shuriken with the light-weight materials mod. It weighs practically nothing and is very cheep to upgrade. Plus it's not a bad backup weapon if you run short of clips for your shotgun. Works surprisingly well on Guardians' mailslots.
For MP I honestly don't have a favourite class (though I'm really enjoying my new N7 Demolisher) though if I had to pick a least favourite, it'd have to be the vanguards...mostly because of the shotgun thing again.
In SP my main Shep is a soldier class, but that's just because on my very first playthough I didn't understand what biotics and tech powers were all about and of course my being stubborn at roleplaying so I never changed her class . In ME3 her loadout varied wildly as I liked to try out the new weapons. By the end of the game though she was rocking a revanent, a valiant, a carnifex and a disciple.