I echo the advice about investing in Warlock. Book of Shadows gives you amazing versatility (pick from any spell list). Plus, as has been stated, Invocations give you that at-will-magic vibe you're looking for. I highly recommend Mask of Many Faces.
Keep in mind that MCing Warlock means you can cast the spells from classes with the "Spellcasting" feature using your Warlock spell slots. This is a Big Deal, because those slots refresh after a short rest. And, at Warlock 3, they'll be 2nd level slots (or higher). 1st level spells cast with higher level slots are often more potent. Sleep, for example, becomes very, very powerful when cast in a high level slot. Note the absence of saving throw.
I caution against grabbing classes just for the boost in # of cantrips. Once you get Eldritch Blast, you really don't need any other attack cantrips. Maybe Shocking Grasp for the "no reactions" feature (it's a good "escape" spell because no reactions = no OAs). Maybe Fire Bolt to start fires beyond Prestidigitation's 10 foot range, and because fire damage is useful. And Sacred Flame is nice for the radiant damage, and because it's a ranged cantrip that doesn't care about cover (obviating the need for Spell Sniper). Okay, I guess there is a need for more attack cantrips.
I'd go for these cantrips first (in order of priority)
Prestidigitation
Eldritch Blast
Guidance
Fire Bolt
Sacred Flame
Shocking Grasp (particularly if you have a familiar)
Minor Illusion
Mending
Starting at 6 gives you the luxury of not having to consider playability at low levels. For max fun, I suggest going 3/3 so that you
immediately have access to all the 3rd level goodies from two classes.
So:
Start as Warlock 3, for Wis & Cha saves. Failing Wis saves often means losing your turn/losing your action.
Your choice of either Fighter 3 (Eldritch Knight), Rogue 3 (Arcane Trickster), or Bard 3 (either, though Lore seems more in-theme).
You could instead go Wizard 2 (School of Conjuration gives a fun and powerful at-will magical ability) + Cleric 1 (either Light domain for Light, or Nature Domain for Guidance or Mending).
I think Eldritch Knight 3 might deliver most bang for buck. Action Surge is amazing with Eldritch Blast (four attacks!); the self-heal, Defense style, and armor & shield proficiencies vastly increase survivability; and the weapon bond is super cool--especially if you bond a thrown weapon, and call it back after impaling someone. Plus you're only two levels away from Extra Attack, making you a melee threat, and thereafter only one level away from an additional feat (like Magic Initiate, presuming you took Spell Sniper at 1st as a human or at 4th on the way to 6th).
Then again... Arcane Trickster gives you 1 more cantrip than Eldritch Knight: the always-useful Mage Hand. Actually an improved Mage Hand: it's invisible, and much more capable. Plus, Rogue can combo very well with Warlock if you took the Mask of Many Faces invocation: put one of your Expertise choices into Deception. On the other hand, Sneak Attack doesn't work with spells.
Tough choice, but really you can't go wrong. Either one, or Bard, would be a blast.
Quick build:
Concept: Master of minor magics. DPR + tank. Uses Eldritch Blast for ranged damage, but not afraid to mix it up in melee.
Str 14, Con 13, Dex 12, Int 12, Wis 12, Cha 16
HP: 42 AC: 21 (plate + shield + Defense style) Speed: 20 (base 30, -10 because doesn't meet Str requirement for plate)
Attacks: +4 (1d8 + 2 morningstar), or +4 (1d6 + 2 javelin, range 30/120) or +5 (two blasts, each at 1d10 Eldritch Blast).
Key gear: morningstar (bonded), javelin (bonded), bat familiar, plate armor, shield.
Key class features: Defense Style, Action Surge, Second Wind, Pact Magic, Spellcasting, Invocations (see below), Weapon Bond, Fey Presence (Charm or Frighten AOE).
Class Levels:
Warlock 3 (Fey Patron, Chain Pact)
Eldritch Knight 3
Feat: War Caster (advantage on Concentration checks, weapon or shield don't interfere with Somatic components, can cast spell instead of OA).
Invocations: Mask of Many Faces (cast Disguise Self at-will), Book of Ancient Secrets (gain Ritual Casting and two rituals, can add any ritual spell to Book of Shadows).
Cantrips:
Prestidigitation (wlk)
Eldritch Blast (wlk)
Guidance (tome pact)
Sacred Flame (tome pact)
Fire Bolt (tome pact)
Minor Illusion (Eldritch Knight)
Shocking Grasp (Eldritch Knight)
1st level spells:
Hex (Warlock)
Dissonant Whispers (Warlock)
Sleep (Eldritch Knight)
Shield (Eldritch Knight)
Magic Missile (Eldritch Knight)
Find Familiar (Book of Ancient Secrets)
Unseen Servant (Book of Ancient Secrets)
2nd level spells:
Misty Step (Warlock)
Suggestion (Warlock)
You can go Warlock 4 and 5 after this for the additional Cantrip (Minor Illusion), ability score improvement (Cha), invocation (agonizing blast), and spells (Vampiric Touch, Hunger of Hadar).
Or can go Fighter 4 and 5 for the ability score improvement (Str, to get rid of speed penalty and add to weapon attack & dam), Extra Attack, and spell (Protection from Evil & Good--like your other Int-based spells, this spell doesn't care about your Int modifier). And then pick up fighter 6 for another ability score improvement, but choose Resilient (Con) to bump your Con to 14 and gain proficiency in Con saves (and net +1 HP per level).
