What low-level arcane spells are directly relevant to combat where my spellcasting ability score doesn't matter?

Question

I'm building a tough front-line Fighter maxed on CON and STR who is not the sharpest knife in the drawer. I'm going with no higher than INT 13 (which I intend never to increase, and would love to let it be even lower), but I want to start by taking a brief dip in an arcane class such as Wizard (probably no more than 3rd level) before going full bore in Fighter. I've got no particular race in mind for the build. I plan to use a versatile martial weapon such as longsword.

My motive is to get a batch of spells where there is no spell attack, no saving throw, i.e. where the low Intelligence doesn't matter (or low Charisma if I go Bard or Sorcerer), but the spell still helps me in combat. (No Eldritch Knight for me; I want to be a Battle Master who uses a bit of magic to be even more of a menace in the trenches.)

Because of my purpose, I want no utility spells. I realize that clever folks can come up with a way for just about any spell to be creatively employed in combat, but I don't want things like Message or Light. For a spell to make my list it has to deal damage, or protect me from taking damage, period. Misty Step makes it in because it lets me escape out of an onslaught.

The list I have so far is:

Cantrips

• Blade Ward
• True Strike

1st level

• Absorb Elements
• False Life
• Magic Missile
• Protection from Evil and Good
• Shield

2nd level

• Mirror Image
• Misty Step
• Shadow Blade

I need a few more. By my reckoning, at Wizard 3 my spellbook will have eight 1st level spells and two 2nd level spells. Are there others that meet my criteria in other published sources? Other classes besides Wizard are OK too. And the more spells I can cast while I'm fighting with a melee weapon, the better.

Answer 1

Don't be a Wizard. Be a Divine Soul Sorcerer.

If you're explicitly not going for any of the utility spells, then you correctly see that there aren't that many good offensive or defensive spells that don't require you to have a good casting stat. My suggestion would be that, rather than going Wizard, you go Sorcerer, with the Divine Soul sorcerous origin (Xanathar's, p 50). In short, this sorcerous origin lets you pick spells from both the Sorcerer and Cleric class lists, as well as giving you an ability to add 2d4 to a save or attack roll once per short rest. You'll have a lot fewer spells, since you're a Sorcerer, but you'll have a lot more versatility in how you cast them.

My suggested spell list up to 3rd level would be:

Cantrips: Booming Blade, Green-flame Blade, Guidance, Resistance

1st: False Life, Shield of Faith, Shield

2nd: Mirror Image

In addition, you get one more 1st level spell depending on your alignment from the Divine Soul sorcerous origin. Law is a good choice for you, since bless gives you extra bonuses to attack rolls. I'd also suggest taking the Quickened and Twinned metamagic abilities, so you can cast while attacking and buff your allies, respectively.

Answer 2

All things considerered you should stick to the Sorcerer

Choosing a spellcaster

There are 8 classes with Spellcasting ability. Additionally, there are 2 subclasses.
Excluding non-Arcane classes and Eldritch Knight (based on information in your question) leaves us with the following list:

• Bard
• Rogue, Arcane Trickster
• Sorcerer
• Warlock⁽¹⁾
• Wizard

Spells of 2nd level and lower listed below under each of the class' section are combat-oriented and require neither spell attack nor saving throw from a target nor use spellcasting modifier for additional effect, such as healing spells. Recommended spells will be emphasised.

Bard

Personally, I really like the idea of a Fighter/Bard multiclass, but class' main feature, Bardic Inspiration, heavily relies on Charisma: the number of Inspiration die depends on your Charisma modifier, on top of this some of the Bard's subclasses' features rely on a saving throw from your target. I personally recommend College of Swords for your character. Multiclassing into Bard will net you additional proficiencies in one skill (any) and musical instrument. Bard's spells:

• Cantrips: Blade Ward, True Strike
• 1st level: Bane, Longstrider, Sleep
• 2nd level: Cloud of Daggers, Enhance Ability, Heat Metal, Invisibility, Silence, Warding Wind

Rogue, Arcane Trickster

Spell list is limited and spell slot progression is 1/3 of a regular caster. Extra 2d6 from Sneak Attack is handy but heavily relies on a weapon you use. Unless you're Rapier&Board fighter that will utilize Color Spray or Sleep during combat, I recommend to skip it. Multiclassing into Rogue grants you proficiencies in one skill (rogue's skill list) and thieves' tools. Rogue's spells:

• Cantrips: Blade Ward, True Strike
• 1st level: Color Spray, Sleep

Sorcerer

@DuckTapeAl already has a good answer. In addition, you can cast Booming Blade using Twinned Spell Metamagic ability to make 2 melee attacks instead of one until you get Fighter's Extra Attack.

• Cantrips: Blade Ward, Booming Blade, Green-Flame Blade, True Strike
• 1st level: Color Spray, Expeditious Retreat, False Life, Magic Missile, Shield, Sleep
• 2nd level: Alter Self, Blur, Cloud of Daggers, Enhance Ability, Enlarge/Reduce, Invisibility, Levitate, Mirror Image, Misty Step, Shadow Blade, Warding Wind
• Cantrips (cleric): Guidance, Resistance
• 1st level (cleric): Bane, Bless, Divine Favor, Protection from Evil and Good, Shield of Faith
• 2nd level (cleric): Aid, Protection from Poison, Silence

Warlock

A solid pick, since both Superiority die and Warlock's spell slots restore on a short rest. Invocations are handy and Pact of the Blade gives you a magical weapon. Choice of the patron relies on your combat behaviour and expended spell list you might like but I personally recommend Fiend for you.

• Cantrips: Blade Ward, Booming Blade, Green-Flame Blade, True Strike
• 1st level: Armor of Agathys, Expeditious Retreat, False Life, Hex, Protection from Evil and Good, Sleep
• 2nd level: Cloud of Daggers, Invisibility, Mirror Image, Misty Step, Shadow Blade
• Suitable Invocations: Fiendish Vigor, Thief of Five Fates, Improved Pact Weapon (Pact of Blade exclusive)

Wizard

Wizard's Arcane Recovery feature allows him to regain spell slots once per day on a short rest. There are numerous Wizard's subclasses but there are few that really suits you, these are School of Divination (for two d20 you can use to replace nearly any roll in your line of sight) and War Magic (for +2 AC or +4 to a saving throw on a reaction).

• Cantrips: Blade Ward, Booming Blade, Green-Flame Blade, True Strike
• 1st level: Absorb Elements, Expeditious Retreat, False Life, Find Familiar⁽²⁾, Longstrider, Magic Missile, Protection from Evil and Good, Shield, Sleep
• 2nd level: Alter Self, Blur, Invisibility, Levitate, Magic Weapon, Mirror Image, Misty Step, Shadow Blade

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⁽¹⁾ - Pact Magic isn't a Spellcasting per se, but I count it as one in the scope of this question.
⁽²⁾ - Using an owl familiar might grant you an advantage nearly on every turn. Also, Find Familiar is a ritual spell so you do not spend any resources.