I'd say it is primarily a question of what your group thinks is more interesting in terms of gameplay and theme:
Dark Heresy is focused on investigating heretical cults or ancient mysteries, and challenges not only the characters' brains and brawns, but their very soul. They will become part of a highly secret organisation protecting the Imperium from threats both natural and un-natural, both from within and without, and will regularly interact with just about any branch of the government and its many Adepta, from Imperial Guard officers and Arbites Judges all the way to Ecclesiarchy Cardinals and Space Marines. Their journeys will take the players into places like dark underhive junkyards, a noble lord's dining room, a Forge World manufactorum and many more. And each of these locations is likely to have its share of dark secrets waiting to be uncovered.
Rogue Trader, on the other hand, is a grand endeavour aimed at amassing ever more wealth and influence by just about any means imaginable, with dauntless industrialists (ab)using the lack of established law and order on the fringe worlds of the Imperium and much farther beyond to stake their claim on the riches of worlds that have never been touched by mankind before .. or whose native inhabitants find themselves unable to resist the strategies of the cunning entrepeneur who knows how and when to apply the power of a massive multi-kilometer starship equipped with weapons of mass destruction, contacts made and groomed with Imperial officials, mercenary forces and underlings, or the untold riches plundered from elsewhere for investment into a new venture.
How much player agency you grant your group depends entirely on you as their GM. Even though by default the Inquisitor is supposed to be an NPC, you can easily run a Dark Heresy game with one of the players as a junior Inquisitor - which might even appeal more to players who join this game with expectations gained from GW studio material or various BL novels about the Inquisition. And just like that, even though by default the Rogue Trader is supposed to be a player character, you can easily run a RT game that sees this position filled by an NPC, who entrusts his inner circle of officers (the players) with specific missions to pursue. The latter is how my own game of Rogue Trader started, even though the NPC Rogue Trader's daughter is a player character and we expect her to ultimately inherit daddy's ship in the course of the campaign.
As far as pre-made starter adventures are concerned, I believe all of FFG's 40k RPGs have a Free Introductory Adventure which might be a good starting point. Just google for the PDF downloads; they should be hosted somewhere here on this very site!
PS: Also, get the relevant player's handbook for whatever game you ultimately decide upon. For DH it'd be the Inquisitor's Handbook, whereas RT has ... Into the Void, I think? They tend to include a ton of useful stuff, much of which actually ought to be in the core rulebook already, and they are really the only books aside from the main ones I'd consider "must haves".