Kind of a random list of thoughts, mostly all competing for bonus actions/concentration. When you run out of summons, you can try these (although you have to cast them before wildshaping):
Flaming Sphere is nice for bonus action AoE damage. You can use it to help you not get mobbed in melee, or move it back to protect your party. It's like having a mini-moving-fireball minion to watch your back.
Dust Devil from EE is the same. Less damaging, but uses Str instead of Dex saves, and offers pushback too. Good for when light or burning things is a problem.
Heat Metal is great for anything in armour. It's extra damage and a debuff all-in-one.
I mostly mentioned Magical Initiate (Wizard) because you wanted a familiar. But as a Moon Druid, you essentially are your own familiar. So you could grab Expeditious Retreat if you wanted. Fast bears are scary bears. It makes other forms nicer to consider as well, even aquatic ones on land. Giant Octopi and Plesiosaurs are actually pretty mobile with Longstrider and Expeditious Retreat cast on them, for some fun reach/restrain related combat shenanigans. Or be a land shark, or a killer whale, stalking its prey across the mountain tops with its blindsight. Or be a mining engineer Giant Badger, and put the dwarves to shame. There's heaps of dumb stuff to do, and using a couple of lvl1 slots for an encounter isn't bad for the hilarity value. Your monk will love you too.
There's very little reason to not have a Mage Hand carrying an open bag of caltrops or ball bearings (or both mixed, 5 pounds is a lot) ready to be poured wherever you want. The save DC isn't great, but the more battlefield control, the better. Thus MI(Wizard) being awesome.
If you really do want Magical Initiate (Cleric), then your lvl 1 slots will go a long way with Bless. Pity the cantrips aren't great. But Bless makes up for it. Just make sure with your DM that you can cast it with normal slots too.
You may as well have an attack cantrip. Produce Flame, Thorn Whip, Acid Splash, Frost Bite, Shillelagh and Magic stone all have their uses. Produce Flame is probably best, with Thorn Whip being close behind (anti-grapple CC).
Faerie Fire anything you want to fight if your concentration is free. Advantage is good.
Out of combat, in caster form, you're golden. Charm Person, Guidance, Enhance Ability, Pass without Trace, even Longstrider all do "stuff" for various situations. Remember to blow any remaining slots at the end of the day on Goodberries though (they'll last into the next day, so you've sort of pre-cast some your healing for the day, freeing up lots of slots tomorrow. Those rest days are amazing for you, for the amazing day after).
Unless it's a particularly deadly one, you can wildshape to tank traps if you're out of summons. Cast resistance (or guidance if you think it's a different save type), wildshape into something tanky, walk up, headbutt trap. Keep casting Resistance if it's a 3 save-or-die poison or something, or change form into something with good stats for that save. But HP sponge is HP sponge, usually with good Con and Wis saves.
Beg your Warlock to cast invisibility on you sometimes. You're a jack of all trades, a tank, a healer, a wizard, but you're a scout as well. Invis+PwT+Wildshape makes you essentially undetectable, but you might have blindsight, darkvision or advantage on perception yourself.
If you've ever got someone entirely incapacitated, and you're going to kill him anyway (or question him fairly strenuously), wildshape into a rot grub and get one of your party members to put you into the badguy's ear. He'll talk. Or you'll eat his brain over the next few days.
Jump and Spider Climb are surprisingly useful, even with wildshape. Be a drop-bear. Be a ninja. Be a ninja drop-bear! It also helps other party members keep up with your shenanigans. You'll be flying at will long before them.
Remember that you can grapple a bit when necessary (you've got Athletics). As forms get bigger, you get better at it. You can also carry a heap when needed. When you can fly, grappling is evil. People can also ride you. You are a Yoshi when needed. A flying Yoshi, later on.
Sleet Storm is a nice CC and anti-magic spell. Dispel Magic is an even nicer anti-magic spell. You should at least have one of them prepared (DM), but maybe both.
Barkskin and Lesser Restoration should pretty much always be on your 2nd level list as well. Tanking and curing what ails people is what you do. Plus lots of other stuff.
Sometimes your DM may say something like "Bears can't do that." Even stuff that they could, if they knew how to. Apes have hands though, 16Str, +5 Athletics and a climb speed. If a bear can't do a strength job, an ape probably can.
Even if you can't do the sensu bean combo, it still might be worthwhile picking up a level of Cleric (Life) at some point. You get bless, can round out your cantrips, make your non-berry related healing better, and get a stack of lvl 1 utility spells. Actually, any domain is pretty good. Depends on the campaign. Consider it at lvl 7 as a flavour choice on how your character is forming up and what you think you'll be doing with him/her. There's nothing wrong with staying mono-Druid either (getting to Moon Druid 8 ASAP is pretty much unlimited flight for the effort), but having a silly amount of level 1 spells that you can change day-to-day, and having Bless as a backup "whatever, combat" spell is probably worth the level regardless. Bless also keeps your forms relevant longer, because they do start to tail off a little bit after this (In combat. Fortunately you're also an awesome caster by this point, with form utility and HP sponge as well). And everyone likes +d4 more relevance, not just you.
For cantrips, I'd pick: Guidance, Resistance, Produce Flame.
For MI (Wizard), I'd pick Mage Hand, Minor Illusion, Expeditious Retreat.
As you can see, there's heaps of options for different situations and spells to use. Probably not enough preparation slots for it all, but Druids are never boring. Powerful, versatile and fairly fun, both in and out of combat.