I am getting involved with a new group in the next week or so.

My source book experience is limited.  However, the new DM says anything in any book is allowed. 

I would like some suggestions for race and class.

Not really looking for something with a title 10 words long.

I generally prefer to play single class and not multi class. Other than level 1 as a class to get certain bonus or skills, then switch to my primary class

 well what type of class do you want to play? do you want to be a tank dishing out hit after hit? go for fighter or barbarian. if you want to be casting powerful spells play like a wizard. if you want to help your party play a bard or cleric (not that clerics help the party :) ). Or if you want to play a powerful melee character with a bit more spice play a paladin. just pick a class that sounds interesting and play it, see how you like it

There was a decently long discussion not long ago about Bugbear as a Ranger, specifically Gloomstalker.

In the new Multiverse book, Bugbears were changed so that they deal an additional 2d6 of damage on every attack they make against a target that hasn't taken a turn yet in combat. Gloomstalker rangers get an additional attack they can take in the first round of combat that also deals an additional 1d8 of damage... so fairly early on you can output a pretty massive stack of damage in the first round of combat. Plus Gloomstalker is probably the best Ranger subclass overall, so even after that first round you'll still be a stellar fighter.

Good question.  I generally tend to not play a tank.  I have played a lot of clerics because nobody wants to play one typically. 

Probably more along the lines of a melee character with a bit more spice. 

Rune Knight Fighter, to me, is probably one of the spiciest melee fighters right now. It's got great features that help not just in combat, but in roleplay and exploration as well. Plus with their Giant's Might feature, they can grow Large... I think it'd be very fun to play as a small race with this class, just to mess with people. I'm partial to goblins because their ability to hide or disengage as a bonus action is incredibly versatile, but Halflings are also fun, especially with the ability to re-roll ones. I'm in a campaign with a Halfing Bard who also has the lucky feat, and he has never once rolled a natural 1 in the entire game, and we've been playing about 2 years.

Rune Knight.  Very interesting.  Cloud Rune.  Could you explain this

In addition, when you or a creature you can see within 30 feet of you is hit by an attack roll, you can use your reaction to invoke the rune and choose a different creature within 30 feet of you, other than the attacker.

So after the attacker hits you or a something else you can have the attack put on another creature.  I take it the other creature could be a creature friendly to the attacker

Yeah, it's great because you can use it to redirect a critical hit and have the bad guy kill his own ally.

Do you want a combination that is good, or one that is fun? They don't always overlap. I don't really have any books other than the basic ones, but, a paladin half elf should be really good, because of the +2 charisma and +1 on two other things, probably should go to strength and constitution. And there's also a tiefling warlock, the +2 charisma is nice, and it combos well with the Infernal Legacy spells. Anyways, I find paladins to be very fun to play, and combining that with any race that boosts your charisma, strength or constitution should be pretty good, paladins hit hard, take hits, and can buff their teammates to also hit hard and take hits, while also being able to buff themselves, they have a nice split between combat and support, which I really like. Having a paladin or cleric works great for any team, specially if you use them with a barbarian or fighter in your team.

As far as race goes, both variant human and custom lineage are good choices, because of the extra feat. Custom lineage is the only race that lets you get a +3 bonus in any stat at the beginning. Mountain dwarf is good as well, as you get +2 on two stats and some other useful abilties, such as darkvision and weapon/armor proficiency.

As far as classes go:

You could try a Moon Druid. That would be a good compromise between an a cleric and a melee character, as you have some spells for healing and buffing in addition to being a powerful shapeshifting melee combatant.

Paladin of Vengeance is also a valid choice, though you may wish to add two Hexblade levels, so you can attack with your Charisma. Alternatively you may also want to go full Hexblade.

You could play one of the more offensive Barbarian variants, such as Zealot.

Battlesmith and Armorer Artificers are melee warriors with some support capabilities too, but they may be a bit too tanky for your taste.

More looking for fun with a sting.