Dungeons and Dragons is a wonderful pass time, but it can be pretty intimidating to get into the first time around. There's tons of information online about the easiest campaigns to DM and tips for actually playing the game, but for most new players picking a class is the most difficult part. The 5e Player's Handbook does a pretty good job of explaining how to play a class, but some are certainly a bit easier than others - both to roleplay, and go through combat with.
While Bard can be a little difficult to get started with, it's a great class for those that want to see some action during combat, but don't necessarily want to be on the front lines. It's one of the easier support roles to play in Dungeons and Dragons, and it has options for players that prefer either role-playing or combat at third level when a Bard chooses which college they wish to be a part of. Plus, they do get some spells - something that always helps spice up the game. It isn't the best class for new players, but it's one of the most fun for those without too much experience.
Rangers get a pretty solid am0unt of customizability fairly early on, plus bonuses against an enemy type of their choosing - even against the weirdest creatures in the Monster Manual, should they choose them. Those bonuses can really come in handy for new players, even though they aren't all directly related to combat.
For campaigns that aren't very linear, or where players may be spending loads of time outdoors, a Ranger can be an incredibly useful tool. Like Bards, they also get access to a few spells, though not so many as to be overwhelming. It's a great option for those that want to role-play as the strong silent type, or basically just be rip-off versions of Aragorn from Lord of The Rings.
Especially in the lower levels, a Paladin is a great front-lines fighter with an AC high enough to ensure they won't die in the first few encounters unless your DM is sadistic. Plus, they can keep those around them alive with a variety of spells, making them a key part of most group dynamics. Picking a god to be loyal to is generally a good time, and there are usually quite a few interesting backstories that can be woven to show how a player's character chose to walk the Paladin path.
That being said, they can be a bit dull to role-play, as they're forced to be Lawful Good in most campaigns. There is another class called Oathbreaker Paladin that characters wishing to be evil can run as, but they get a bit more complicated. Still, Paladin is good for new players that don't want to immediately have their heads ripped off by Ogres.
Fighters are capable of putting out an impressive amount of damage, but also have some self-heals that will keep them alive on the battlefield. They won't immediately have access to any spells, but it is possible for those that take the Eldritch Knight Martial Archetype, which without diving into the specifics, will make the class a bit more daunting, but still fun to play. The base loop of Fighter will pretty much always be "fight things", but that isn't a bad thing. A lot of the time, players will fall into tropes as far as role-playing is concerned, but it's still possible to have plenty of fun as the grizzled warrior seeking their next brawl.
As a Barbarian, the only real goal is to make sure that everything that should be dead, is dead. This makes it, arguably, the easiest class to play, as the goal of smashing things with a hammer or slashing them with an axe is easily digestible to most. Pretty much all of a Barbarian's abilities are tailored towards maximizing damage output, making them one of the deadliest classes on the battlefield - at least as far as martial combat is concerned.
Most Barbarians tend to lean towards the more chaotic, and, well, evil side of the alignment spectrum, but they can still be pretty fun to role-play as. Who doesn't like being a loveable oaf that could rip someone in half? For those just starting out with Dungeons and Dragons, or anyone with a bloodlust, Barbarian is a surefire way to go.
There are still plenty of other classes for players to choose, and they aren't all confined to the Player's Handbook. One great tip for Dungeon Masters is to allow players to experiment with their characters, especially as they grow more accustomed to the game. While that may not be wise at first, it always makes for a more interesting time after a few PCs die off.