Jo, I did what you are wanting to do several years ago. First of all I went thru the inks that I had and I stamped with them all, using different stamps and papers, testing what I liked and what I didn't. During this process I discovered that I really, really liked water based dye ink pads the best. Thats not to say they are the best ever, just the best for me. I love trying techniques and I found these types of inks to be the most versatile to me. My final choise, based on accessability to actually buy the product at the time, was SU! and Distress (for very much the same reasons as Kristy Tyra I chose two very similar products). Having chose these inks as my mainstay I then stuck with rubber for my stamps.
I don't use Copics so I have no personal experience with them, but from all that I've read here at SCS, Memento is a top choise. And since Memento is also waterbased it should be useful for doing a variety of techniques.
I have since sold off all the other odds and ends of ink pads, and have a neat and tidy ink pad collection that I use all the time. A few months ago I branched out and added Archival by Ranger, as my permanent ink of choise, so now I have three ink collections. All inks come with reinkers.
Good luck with finding your preferred brand. It'll be worth the effort and expense to find your perfect match.