On the issue of "lack of resources", the Voyager
was infamous for not having much of that. Stranded far away from home base, damaged severely in the process, she quickly managed to overcome all logistical shortcomings. Apparently, after spending a few years in Kazon territory where a ship with damaged replicators could achieve little, the crew finally reached a civilized world that could help them repair those devices - and after that, the ship was in want of nothing. Entire shuttles could be created out of thin air in a matter of days or weeks at most!
Whether any starship in the 24th century is created to do something specific and deliberately made unable to do other things, we don't know for sure. Even the tiny Equinox
, explicitly belittled and said to be dedicated to planetary research, was a formidable combatant that almost outfought the Voyager
What we know of the Intrepid
class includes two unique things: she's very fast at warp, and she's very agile in the Badlands. Every other attribute the ship might share with other types: the ability to land, the ability to fire torps and phasers, the use of gel-pack computing systems and Class 9 warp cores and whatnot.
Fast, agile and decently armed would be good for a military scout or a courier. Ability to land would perhaps make extensive scouting of planetary targets easier; things like colonization or supply would probably call for a ship with bigger and more easily accessed cargo holds... The presence of an extra auxiliary craft under the forward hull might boost scouting abilities, too. And the demonstrated self-sustenance would qualify the ship for frontier operations rather than short-range sorties.
Beyond that, the mission profile of the ship is anybody's guess - but we have seen two missions chosen by Starfleet already: the Maquis hunt, and the long range diplomatic courier mission in the DS9 episode "Inter Arma".