There are no classes, but rather sort of "Archetypes"- Mage, street samurai, hacker, face, rigger, weapons specialist and so on... That said, it's entirely point buy character creation (You buy everything- your race, attributes, skills, equipment, connections, magic spells, cyberwear and more...)

The problem with people waiting for other to finish their turn, comes from two sources:
1) 3 "interaction environments": There is the real world, the astral world (Accessible by mages) and the matrix (Accessible to those appropriate cyberwear and programs). the two later environments require quite a specialization, so usually only one person is active in them, which means that when someone goes on the astral, or on the matrix, they usually go alone, and the rest need to wait for them to finish their thing. Sometimes it's short, sometime less so... The matrix especially feels highly technical and a sort of a mini game, so unless the rest of the players understand the rules, it's basically listening to nearly an entire different game. The astrl is less of a problem, since it draws from imges known to all. Mny groups used to "hire a hacker", which does things in the background, though recent additions tried to simplify things, and also include challenges that involve the entire team (A battle while the hacker does his stuff on the matrix), but it's a partial success at best.

2) Phases: Some characters gain the ability to gain more than one action phase per round- 2,3, or 4 phases even. This can happen in combat (Martial artist or Heavy Cyberwear warriors, or by magic), in the matrix, or in the astral. This usually comes down to some people acting more, some less, sometime to a considerable, amount. Which in turn, makes those with less action phases to wait for those with more.

The solution however is quite simple- just remove action phases. This has an added benefit of getting the characters investing in these (As action economy is king, you HAVE to invest in them to remain competitive), to choose other mroe interesting, and mroe varied options.