Five-year missions, expeditions into the unknown, seeking the Northwest Passage- these are stories of exploration and RIFTS has plenty of room for those who seek to make known what is unknown.
The core of a campaign focused upon exploration is that the players assume the roles of individuals who are either trained for exploration, or they are specialists of a different--but necessary--sort assigned to such a task. The specific venue varies widely--overland, oversea, undersea, space, planar, etc.--but the format is the same: a team of explorers forms to investigate what, if anything, lies beyond a given threshold. This can be a mountain range or other significant terrain feature, space itself- you get the idea. Adventures are built around penetrating this threshold and then seeing what is there; making first contact with locals, mapping the territory explored, and preserving this information long enough to report back to their patron(s) so follow-up expeditions can be made with the benefit of that knowledge.
Exploration campaigns, therefore, are mixtures of diplomacy and adventure on a dangerous and unknown frontier. Players should be working with low amounts of information, dealing with material scarcity due to being at the tail end of a long logistical train (so they can't operate at optimal efficiency or effectiveness most of the time; this is "count your rations and arrows" territory), and have to deal with constraints that players in other campaigns either don't have to worry about or never even realize exist. Figuring out how to compensate for these scarcity issues, often by interacting with the locals and learning their methods, is part-and-parcel of a properly-executed exploration campaign.
The other issue with an exploration campaign is that what often follows is either exploitation of natural resources, or population movements into colonial settlements, and either development not only strains extant relations with the locals but--unless reversed--inevitably pushes back the frontier as Civilization (i.e. whom the explorers represent) comes in to fill the void that a frontier represents. You can either end a campaign when this phase of exploration arrives, or you can roll with the punches and take the opportunity to shift the campaign in a different direction; each primary exploration expedition, each first contact situation, each push into the unknown presents an opportunity to find something heretofore unseen and unknown to the players. New mysteries to solve, new cultures to interact with, new lands to investigate- this is the feature that keeps it fresh for years on end. Exploit this feature whenever things start to flag.
Exploration campaigns are best done the old-fashioned way: the sandbox. The GM should decide on the region to explore, and set up initial sets of circumstances (including what Occupations, technologies, etc. are allowed to players), and then let them interact without any concern for narrative logic of any sort- the players will, without fail, fill in all such voids with their own notions and thereby succeed or fail without so much as a word out of the GM's mouth. (And that is the other side to all of this: expeditions fail, often disastrously. If they want to be the Donner Party, let them.)
This is a model where your Men-at-Arms will not be so heavily represented, and your Men-of-Magic/Psychics will be likewise reduced in prominence, in favor of Adventurers and Scholars. You need Wilderness Scouts, first and foremost, and then Scholars and Scientists (including medical experts and technicians) with focuses on field operations (which is done by skill selection and equipment choices; someone that needs a big-city lab is not the sort to send on such things, unless it's based out of something like a starship, and that likely means such an individual will be a NPC). Generalists will be more prized members, speaking of Armsmen and Magicians/Psychics, over specialists and time-limited augmented individuals like Juicers are bad choices- as are those tied to logistical trains (Cyborgs) or already unstable (Crazies). (This, again, is where the magical sorts have an advantage so long as magical power is in sufficient abundance.) Problems are better solved by talking or fixing than by fighting, most of the time, and running is not a bad idea- players cannot presume that whatever they face they can handle.
Exploration campaigns are also easily transitioned into and out of because the core of the campaign's paradigm is inherently unstable, and thus temporary, so you can use an exploration phase as a change-of-pace for another campaign when you see the need for such a thing. If you start as exploration, but the players are not interested anymore, it is not hard to let the frontier shift away from them and let them take up positions in the emerging post-exploration communities that arise in the wake of successful exploration expeditions. When devising what to do with a game of RIFTS, don't count exploration out; even as just a temporary phase, you can really get to the heart of what makes tabletop RPGs special by returning to the origin of the hobby- exploration of the unknown, be it for gold, for glory, or for getting away from where they came from.