I've used http://getharvest.com in the past and I think it works really great. Both on invoicing and time tracking. Haven't tried the payment part though.
This hasn't been released yet, it is invite only atm. But at least the site looks pretty good: http://invoisse.com/
AngularJS clearly has the most open tickets which also might mean high level of activity and interest (or being the most buggy framework, but I seriously doubt that =) )
I agree with Dimitris: you'll be fine with basic JS knowledge. Although I would describe the AngularJS learning curve as Ben Nadel puts it in his blog =) (which by the way is a great resource for learning a bit more advanced AngularJS) http://www.bennadel.com/blog/2439-My-Experience-With-Angular...
I can also recommend the screencasts at http://egghead.io/lessons to get a hang of the basic AngularJS concepts (site seems somewhat broken now however...)
This hasn't been released yet, it is invite only atm. But at least the site looks pretty good: http://invoisse.com/