Some passenger missions are wanted criminals, some are not, though some list 'secretive' as a trait, which means passenger satisfaction will drop if scanned. For someone new to the transport game I'd recommend avoiding the former, but the latter is pretty easy to overcome once you know how to avoid scans (speed, low heat, heatsinks, controlling faction relationship, etc) All the potential pitfalls are in the fine print however, and if you pay attention to the missions you're accepting you can easily avoid falling in to a bad situation. It seems every time I am about to choose the cabin, I hit back to triple check exactly what I am signing on for. Do this, and you'll be fine.
I run a lot of transport missions. Mainly bulk haul in a Krait II, which are missions like 54 Businesspersons Seek Transport, sightseeing in Orca or Dolphin (Ben Dover Seeks Sightseeing Adventure) and rescue missions in incursion systems and burning stations (these have fluctuating availability). I don't do much of the one-hop VIP transport or the very long-range sightseeing, but will if it pays especially well.
Passenger missions are nice for a few reasons. One is they are pretty peaceful, with rare interdictions. They tend to pay well. The money seems less than it used to, but many have G5 mats and Rep+++++ as rewards. As mentioned you also are often sent to some of the best spots in Elite. Often, these destinations feature valuable planets like earthlikes, water worlds and ammonia worlds. Stick these with probes to boost the profits on your passenger trips.
If I had one piece of advice for my prospective competition in the passenger hauling game, it is to ignore any requests made by your passengers. That doesn't mean to just not do what they are asking, but to not even open the message. Ignore completely. I've hauled many thousands of butts and have zero ejected or disgruntled and it's because I am careful with which ones I choose and I then ignore the passengers entirely until they disembark.
My passenger ships
Bulk Haul and Rescue (swap stuff out for rescue and it seats 100 in ecocabins)
Parabellum Krait II -- Armed Merchant Cruiser / Rumble Bus
Sightseeing, smuggling and mixed roles
Sunburst Orca -- Interstellar Style Magnet
Interstellar Overdrive Dolphin -- Sightseer / Criminal Smuggling
The Orca and the Dolphin are both engineered to run frosty to help avoid scans. Both idle at 13% heat or lower. Keep a large variety of cabins on hand, and don't forget to look over the missions at the bottom of the board you do not qualify for. Often, a quick cabin change will open some of those up for you.