Conjure Animals is an awesome spell for lvl 3. Just summon swarms with it. 8x 1/4CR swarms are amazing at character level 5 and can stack damage to pretty silly degrees. Cast it as a level 5 spell for 16 swarms(!), and it scales more from there. 1 action to cast, 1 hour(!) concentration duration, and they follow orders, so you can auto-pilot them. Bards, especially Lore Bards (level 6 cross-class spell? This is the one you pick, every time) can sneak the spell in as a class spell too. Here's some options:
Swarm of Ravens: 2d6 damage, +4 attack, 50' flying, reasonable perception. The best all-rounder for higher damage.
Swarm of Bats: 2d4 damage, +4 attack, blindsight, 30' flying. Nice for anti-invisibility work. Eeeeee! Thump!
Swarm of Rats: 2d6 damage, +2 attack, darkvision, smell. Mmmm, smellovision. And darkvision. Might be worth some research time to try and work out how to conjure terribly poisonous or diseased rats.
Swarm of Insects(Beetles): 2d4, +3 attack, burrowing speed 5'. It's at 1/2CR, so you only get 4 of them, but burrow is handy sometimes. If you know they're coming, set land mines. Or just dig through stuff after giving "reasonable" orders. Beetles are dumb though.
Apes: 2x 1d6+3, +5 attack, 30' climb. 1/2CR, so only four of them per upgrade. Well, apes have hands, so they can carry things. They can also throw things. Like rocks. Or poo. Damn dirty slave ape army.
4x rocks-to-the-head followed by ape-grappling or punching is nice. They do come with 2d4 rocks in theory (MM thrown ammo amounts for creatures), so you can plink with them if needed. But having hands makes them BEASTS
for whatever you need done. They're not dumb, so cast Speak With Animals before you conjure them and speak to them in their own language. Then, they'll do whatever. They have to anyway, but no misunderstandings with certain swear words.
Riding Horse or Warhorse. 8 horsies or 4 war-gee-gees are sometimes very handy to have on-call at a moment's notice. It's only for an hour, but at least you've got a getaway vehicle whenever you need one, for the entire party. Also handy for pack mules. When you loot a place, you take EVERYTHING!
Remember the Warhorses' abilities. Move 20' then attack with at least 1 of the herd. It can put lighter enemies into prone/trample lock. They're good fighters, and they're Large
beasts, so they can carry heaps. Maybe fey warhorses like carrying treasure? I think they do
Anyway, the spell is amazing and versatile enough for virtually any situation. Starting at a potential 8x2d6 attacks on anything (ravens) with plenty of resistances and immunities, you're laughing. It scales beautifully, lasts ages, and can get some really cool buffs as well. It also works as battlefield control in the sense that once you've swarmed something, they end up with plenty of AoO against them if they move, but they die if they don't anyway (ravens have 5' reach, but can only attack in their own square). Flying pseudo-damage-wall in a way, but one that can concentrate its damage, move it, or disperse it as needed.
Works with a Conjuration Wizard's lvl 14 bonus (8x45+ HP minions? Nice...) and basically breaks the action economy. There's other creatures to summon, but swarms are probably the best. You can't get the temp HP on swarms, but everything else does. It's like having a backup party of animal slaves, whenever you need them, for any task.
Conjure minor elementals is good for getting around resistances, but this scales quicker when that's not a problem, and has plenty of cool options anyway. Oh, and they'll always release more Monster Manuals, with more under-CR'd swarms and creatures in them, so this spell will keep getting better as 5th Edition matures.
ps. Don't forget Dinosaurs. They're beasts too, and need some love. Because a one action "make dinosaurs" spell is funny. Hopefully there will be more dinos in future MMs. A flock of Pteranodons is cool. Just for giggles really.