DMS, eDiscovery, billing and file sharing are typically separate functions and I don't know of any software that does all of that. Even if there was, I would worry about it being a jack-of-all-trades but master of none. DMS systems are focused primarily on long-term storage and version control where as eDiscovery has to do with cataloging and analyzing documents usually for trial prep. I don't know of a DMS that also does eDiscovery but maybe others do.
We use iManage for DMS and are generally happy with it (if one can be HAPPY about document management, that is). It works well enough but, like most DMS systems, it relies on Office add-ins. Add-ins always add complexity and increase the need for control over software versions. In other words, certain versions of Office only work with certain versions of the add-in and Office patches often require add-in updates. I don't know of any DMS's that don't use add-ins though. That's just the way things are.
We use various systems for eDiscovery, depending on the case. Sometimes
the client has a system (usually web-based) they want us to use and sometimes we use what
we have in-house which is currently LexisNexis Concordance or CaseMap. People complain about all the eDiscovery systems but I think it's more the unpleasant nature of discovery than an indictment of the software.
I won't mention what we use for tracking billable time because it's universally reviled here. It works and accounting is able to bill clients. That's about the best I can say.
For sharing, we just send smaller files via email. For bigger stuff, we use Sharefile which people seem to like pretty well.