I am reasonably familiar with both making decent fighting characters and making decent magic characters, but I've never stepped out of the forefront and taken on the role of support!

I'm curious as to what the "best" build for buffing your friends is? Not just healing but spells that make them hit better/harder, and utilities. I'm thinking the character who the players turn to for things that aren't combat, and who makes them better when they're in combat.

What class/multiclass works best? What race, spells, and abilities do you utilise? How do you spend feats/ASI's?

It'll be between Bard and Cleric with Druid picking up third place and honorable mentions for the Paladin and maybe the Artificer. Something like two levels of Fighter for Action Surge can be cheesed in if we look at a full 20-level build, or we could try to squeeze in three levels of the aforementioned Paladin (going Crown, likely) or Artificer (Alchemist for funsies, Battle Smith for the companion), but I think by and large you want to get to the Bard's or Cleric's higher level abilities sooner rather than later and certainly if you don't know to which level the campaign will go I'd suggest single classing at least well into tier 3. Any caster who chooses spells to support others can at least be a solid option, but other than Druid I don't think anything can really compete with the big two. Druids are certainly no slouches for support, but for me Bards and Clerics still have an edge.

The best build is without a doubt a Peace cleric, since the Peace domain is built for support and is just broken. If your DM allows it, look no further. Other, more reasonable domain options include Twilight and Life. Load up on buffs and spells that can otherwise help the party (control counts for that as well!) and Bob's your uncle.

I'm a fan of bards though, and Bardic Inspiration is incredibly versatile. Best colleges: Creation (the mote of potential enhances your inspiration, crafting something out of nothing is amazingly helpful, and any kind of pet can go help others as needed), Eloquence (enhanced inspiration as well, and debuffing targets for others to go after is great) and Lore (extra skill proficiencies are golden for being able to use the Help action, you get a debuff and additional Magical Secrets to go steal support spells from other classes). I'd go with Creation or Lore depending on whether the party ends up having to improvise often (Creation) or gets to be always prepared boyscouts (Lore).

For race, anything that helps with the right abilities (Cha and Wis will be the big ones depending on your class, but don't discount Dex - initiative matters for support as well) and anything that provides more skill proficiencies. DMs will not always allow you to use the Help action without proficiency, and being knowledgeable about things is incredibly helpful to the party as a whole - knowing a creature is immune to certain things or has a special attack without having to find out in combat first will make a big difference, for instance. Half-Elf is phenomenal for Bards.

ASIs/feats: keep your casting stat up of course, and take feats that are supportive. There's quite a lot of those really, but Inspiring Leader, extra spells and more/better skill proficiencies are the standouts.

I would say the best support character is something like a cleric or bard.

Access to things like healing word and cure wounds is great for healing. Both have access to bane (great for debuffing enemies), clerics have bless to give your party a greater chance to hit and save. Bards have inspiration for those important rolls. Clerics also have death ward which is great for those tough fights, allowing the frontline people to stay up another hit.

Bards are great for out of combat stuff, thanks to jack of all trades, whereas clerics are great at buffing people for rolls all the time (thanks to guidance resistance [both cantrips]), bards only get a set amount of inspiration.

I'm bias towards clerics, but you can make several classes support, pick which one you like the spell list and class features for.

I played in a game with a great support character, they where roleplayed constantly providing words of encouragement, giving little inspirational quotes. A supportive hug or a pat on the shoulder and as often as possible tried to help every character with what they tried to do :). 

Class wise they where a barbarian. Proof you can be supportive no matter what your class ;)   

Divine soul sorcerers have access to most of the best arcane and divine buffs and they get metamagic. You can do some cool stuff that no one else can with that. Twin haste, reach heals, that sort of thing. 

I don’t have decades of experience, but I’m enjoying playing Druid.

I have lots of spells that can impose Restrained, which can set the wizard up for Fireball.

I recently learned Elemental Bane, which scored extra damage on two or three turns per round in the last fight. An automatic 2d6 x 3 as long as the other PC’s spells do at least half damage is better than Fireball, and can last multiple rounds if I maintain concentration.

I’ve heard people think druids are underpowered. But what they lack in combat they make up for in exploration utility. Last dungeon, whenever we got stuck, I just Stone Shaped my way through. Wild Shapes are also great for scouting and stakeouts, as no one suspects the quiet mouse in the corner.

Straight class I would say Cleric and Bard rule the roost for support, but lately I have been looking at a War Cleric/Ranged Battle Master Fighter combo.  The support spells of the cleric mixed with the battlefield control abilities of the Battle Master seem pretty cool.  Bonus Action Spells like Healing Word to get downed characters back up, Spiritual Weapon to add extra damage, and Shield of Faith bolster the AC of an ally leaves your action available to still attack so you can use your Maneuvers to Distracting Strike or Maneuvering Attack to do even more support while still doing damage to the enemy.

Probably not the most effective build, but still seems like it would be fun to play (at least for me).