Balance technically speaking will probably never be achived, practically it can get close.
Elites weapons balance is currently a bit upset by the engineers update and is getting slowly adjusted.
Roles - As in various utilities and degree of difficulty yes. Roles - as in healing, crowd control and dps, not really but can be arranged with engineers.
Best shield weapons are probably plasma and railguns. That is not counting the fact that they are more difficult to use however. The more popular anti shield weapon is lasers of various tastes.
Best weapon against armour is cannons and dumbfire missiles (Their utility at a shieldless target rather than direct hull damage), but they are hard to use. The most popular is therefore multicannons and now perhaps seeking missiles too. Plasmas and railguns also shine to some degree, but less because of hull damage and more because their high piercing value allows them to bypass armour more and affect modules directly.