I am a big fan in doing the dips into different classes. Since our campaigns dont ever reach the super high levels, there isn't really any incentive to look towards the level 17-20 class skills. As a result of this, I normally do dips into classes for the early class skills.

Good for 1 level dips: Fighter, Cleric, Barbarian/Monk (only for the unarmored defense with con/wis), Rogue, Ranger

Good for 3 level dips: Bard, Ranger, Rogue, Warlock

Fighter: is a great starting class for 2 reasons. First is it gets access to all weapons, armor, and shields. Second, is it gets a fighting style at first level. My personal favorite is archery, especially if you are maining a class that doesn't focus on melee combat. the +2 bonus to hit is absurd, and heavy crossbow makes this a very solid damage option for a support character (especially if they don't get multiattack). With full casting characters, you don't really lose out on spell slots with only a 1 level dip (some may disagree here, but that is just my opinion). This is one to do as your first class though, as you don't get heavy armor from a dip, only if you start with it, if you don't want that, go for the dip. It can also be decent for a 3 level dip for the champion archetype (19/20 crits), but I don't have issues figuring out who would want that. Maybe rogue, but pure rogues are generally better in my opinion.

Cleric: is very good for a support character as well. While you dont gain any real bonuses in proficiencies from the multiclass, you can gain access to the cleric's domain, which get some rather large bonuses. I went with the disciple of life, because i wanted to boost the bard's healing power. But other disciples to look at are the war/tempest domain, for the bonus action attacks wisdom mod times per day, knowledge domain for the languages or proficiency, and nature domain for the druid cantrip and proficiency.

Barbarian/Monk: Both of these achieve the same purpose for a 1 level dip. That purpose is unarmored defense. This is very useful for classes that have spellcasting that prevents you from wearing armor, or classes that want to be very stealthy.

Rogue: Expertise is great, and having access to thieves tools is fantastic. Otherwise, not much here.

Bard: I would say the 3 level dip is only worth it if you are going for the college of lore for the extra proficiencies. Jack of all trades is good. It also gets expertise at this level which is once again fantastic. This one is a better way to get expertise than rogue if you are a full caster, as bard wont cut into your spell slots.

Ranger: Good for the 1 level dip for similar reasons as the fighter. Gets a fighting style, and also favored enemy. Loses out on heavy armor however. That doesn't bug me, but it might mess with some setups. This is also better to take as a dip than fighter at a later point, because it doesn't lose out on as much. 3rd level is where it gets great though. The hunter archetype is fantastic for colossus slayer. 1d8 extra damage every turn against enemies that don't have full health, which is great. You are also a half caster for the spell slots, so a 3 level dip wont be bad for a full caster setup.

Warlock: This might be a bit more of a personal one than the others. Eldritch blast is a great primary damage dealer for a class that doesn't have great range options, and it scales as you level up in general, not off of warlock level. You also get access to your pact at 3. Chain is good as your familiar can distract your enemies to give you flanking (good for rogues with sneak attack) and the familiars are good for scouting/roleplaying purposes. Pact fof the blade is good to make a magic weapon, and have the ability to always have your weapon on you, even when you shouldn't. At 2nd level you also get your eldritch invocations. There is a lot of variety here and can mesh well with your other classes (Devil's sight and mask of many faces are my favorites).