Create Bonfire (source XGtE): This spell is fantastic for the druid. It matches the damage of Produce Flame, it can do ongoing damage if enemies stay in place or moves into the square, and the Druid has very few spells which require Concentration at low levels so the Concentration requirement isn't a significant hurdle like it is for the Warlock. If you position yourself well, you may be able to use this with Thorn Whip to repeatedly pull enemies into the square for additional damage. This is a great introduction to area control spells, which is fantastic because the Druid's options for area control are some of their best spells.
Frostbite (source XGtE): Low damage for a cantrip (d6-based), but the big appeal is Disadvantage on the target's next weapon attack. Unfortunately, it works on Constitution saving throws, and those tend to be relatively high compared to other saving throws.
Guidance: As long as you're not concentrating on something with a long duration between fights, you should use this constantly on your allies. Your Rogue should have Guidance for every skill check they make while searching, sneaking, handling traps, etc.
Infestation (source XGtE): Constitution saves tend to be high, which is this spell's biggest problem. The damage is low but fine, and the forced movement is enough to make it useful by forcing enemies to move around in dangerous places or move out of a grapple despite your lack of control over the direction.
Magic Stone (source XGtE): At low levels, a spell attack dealing 1d6+Wisdom will be more damage than any of your other cantrips. But every other damage cantrip will match it at level 5, and without Extra Attack to let you throw more stones you'll never get more than 1d6+5 damage. On top of that, casting Magic Stone consumes your Bonus Action, so it's difficult to use in conjunction with other options. Your best bet is to get three NPCs to stand behind you, pull rocks out of your hand, and throw them at enemies while you use your action to do literally anything else.
Poison Spray: This highest damage die for cantrips, but has problems: only 10 ft. range, and it works on a Constitution saving throw, so enemies will frequently resist it.
Primal Savagery (source XGtE): More damage than you can get out of any other Druid cantrip
Produce Flame: The Druid's go-to damage cantrip, it notably also allows you to hold the flame and carry it around as a light source. You should be able to light fires with it even though that function isn't specified in the spell's text. You are holding a flame large enough to cast twice as much light as a candle, after all.
Shape Water (source XGtE): This is as abusable and versatile as Prestidigitation. Freeze a solid 5 foot cube of water and drop it on someone. Pour water into a lock, freeze it, and allow the ice expansion to break the lock. Put a dome of ice over something you're protecting. Build a small bridge in 5-foot segments. Block a hallway. Freeze a door in place. The uses are numerous and fantastic. If you have a barrel of water and this cantrip, you have a solution to most problems. Honestly the fact that this spell is so much better than its other elemental equivalents (Control Flames, Gust, and Mold Earth) is a good indication of just how awful those spells are.
Shillelagh: use this only if you are out of Wild Shape slots. the most damage you can ever get from melee attacks is 1d8+5 (avg. 9.5), which will be matched by Produce Flame at 5th level (2d8, avg. 9).
Thorn Whip: The damage is fine, but the real appeal is the pull effect. 10 feet may not seem like much, but its enough to pull enemies off of ledges, to pull low-flying enemies into melee, to pull enemies into an area control effect like Create Bonfire or Wall of Fire, to pull enemies out of a grapple, or in a pinch you can pull an ally out of a dangerous location (albeit at the price of some friendly fire).
Thunderclap (source XGtE): Damaging every creature within 5 feet of you is great if you're in melee facing numerous enemies. Even with Extra Attack you will deal more damage with this against three or more foes than you could with a weapon. See my article on Melee Cantrips vs. Extra Attack for a breakdown of the math comparing melee cantrip spells to normal martial attacks.
1st-Level Spells
Absorb Elements (source XGtE): A fantastic defensive option at any level, this will save your life when you encounter an unpredictable source of elemental damage like as a trap or a spell. The bonus damage on your next attack is largely useless, but it still feels cool when you use it.
Create or Destroy Water (source XGtE): The ability to magically create water has many uses. Few of them are combat-related, but combined with Goodberry and an appropriate plant, this allows you to be fully self-sufficient.
Cure Wounds: More healing than Healing Word, but the action economy is considerably worse. Save this for when you need hit points and you're either out of hit dice or don't have time to rest.
Detect Magic: Someone needs to have it in every party.
Entangle: A great are control spell at any level. Strength saving throws tend to be low for any creature that isn't a gigantic Strength-based brute, so it's easy to restrain even high-level enemies. However, it requires Concentration so you can't easily combine it with things like Create Bonfire.
Faerie Fire: The lowest-level option to deal with invisible creatures. Hopefully you won't run into any at 1st level, but but it's important to have some way to deal with invisibility just in case.
Healing Word: More important than Cure Wounds, especially at low levels. As a bonus action you can heal an unconscious ally enough to get them back into the fight, and you still have your action.
Goodberry: Not useful in combat, but more healing per spell slot than Cure Wounds. Dump all of your spell slots at the end of the day into Goodberry so you have a giant bag of healing to use between combats the next day.
Longstrider: A helpful buff for highly-mobile characters, and with an hour-long duration it can be a great use of low-level spell slots once your 1st-level spells start lagging in combat.
Thunderwave: With the exception of Gust, this is one of your very few options for pushing enemies away from you. It's especially appealing if you can push an enemy into an area control effect, but otherwise it's not a good go-to option for damage output in combat.