1. For The Good Of Mankind, Set It In The Future
I obviously don't mean our future. That much should be obvious. I mean to set it further in the future than any other Star Trek series. It needn't be by much, but Star Trek has suggested many technological improvements over the years and because of this to try to set it authentically in a period between the series would constantly remind viewers that technology hasn't moved that far forward. For example, if a new series was set between the Kirk years and the Picard years in the "Lost Era" then you wouldn't have things like PADDs which itself is silly as we already have them in the form of tablet computers. The Abrams films are an example of this the communicators used in that particular future look less advanced than my smart phone and the ship's control systems looks like Microsoft Surface. By moving further forward into the future this can be avoided and Star Trek can once again help to influence the technology of the future. There is currently an XPRIZE for the development of a working medical tricorder, there is a lot of hype about Google Glass (said by Google to be influenced by Geordi La Forge's VISOR - although I think it more closely resembles the devices used by the Dominion), 3D printers are becoming more normal (similar to replicators with NASA aiming to create one that dispenses food). But it has been a while since Star Trek suggested anything new along these lines Deep Space Nine, Voyager and Enterprise each brought nothing significantly new to the table which has seen developments in the realm of technology. By moving it further into the future it removes the restrictions on the writers and allows for Gene Roddenberry's philosophy of "technology unchained". If Star Trek could be a muse to developers and companies before, then let it be again.