“, remain VFR” — may I enter Class C airspace?
Yes, you were allowed to enter the class C in that case, but you weren't cleared to do it because no clearance is needed to operate in class C, just communication with ATC. The AIM 3-2-4 has the best explanation of this (see also the basic regulation in 14 CFR 91.130):


  
  If the controller responds to a radio call with, “(air craft callsign) standby,” radio communications have been established and the
  pilot can enter the Class C airspace.
  If workload or traffic  conditions prevent immediate provision of  Class C services, the controller will inform the pilot to remain
  outside the Class C airspace until conditions permit the services to
  be provided.
  It is important to understand that if the controller responds to  the initial radio call without  using the  aircraft identification,
  radio communications have not been established and the pilot may not
  enter the Class C airspace.
  


So if the controller used your callsign then you've established radio communications and you can enter. This also applies to class D but not to class B, where you need an actual clearance to enter. (This is a classic exam question/scenario, by the way.) As @rbp suggested, the instruction to "maintain VFR" was probably the controller's way of letting you know up front that he was too busy to give you a pop-up IFR clearance or whatever else you might have wanted. (Maintain is an official ATC term, remain is not, although the controller may still have used it accidentally.)

As for flying into busy airspace, it's up to you as PIC to determine what's safe and what isn't. If you had the HSV ATIS (so you can anticipate traffic patterns), were squawking 1200, were in communication with ATC and were keeping your eyes outside the cockpit then there's not too much more you can do (you could turn on all your lights if you think you need to make yourself more visible). But, if you ever feel unsafe or uncomfortable in any flight situation then you shouldn't hesitate to take action - like staying clear of the class C for a few minutes - if you do feel it's necessary, that's simply part of gaining ADM experience.