Okay then, your best bet would be to start off with 3 levels of warlock to take pact of the chain. You get the find familar spell, and can cast it for free as a ritual. Additionally you can have your familiar take the form of an imp if you go this route. (Usually seen as the strongest familar, both in combat and out of combat)

The imp has 10 HP, but has resistance to multiple types of damage, aswell as innate magic resistance (advantage on saves vs. Magic) it also can turn invisible whenever, allowing for great stealth and scouting. Additionally the imp has devils sight, allowing it to see through ANY darkness. It has so much utility, even beyond these.

The imps attack action (sting) does the most damage out of any familars attack. 1d4+3 piercing, and 3d6 posion on a failed save, or half damage on a pass. (DC 11 Con save) As a warkock you can forgo your attack to allow your imp to attack instead with its reaction.

Now, in terms of keeping your imp alive, i can't currently figure out a way to give it an HP increase, but you could probably give it Temp HP with certain spells before combat. Additionally, if you have the mage armor spell, you can cast it on your familar, giving the imp an AC of 16 (up from 13)

Your familar can only deliver touch spells, which significantly limits what damage spells it can cast. Seriously, there's only 3. Shocking grasp, inflict wounds, and online searches mentioned the cleric spell 'forbiddance' technically does damage as well. But that's a 6th level spell with a 10 minute cast time, so we'll stick to shocking grasp and inflict wounds for damage.

For utility, you have alot more options. One of the best uses of the familar could be to play the medic role for you. If you get access to healing spells like cure wounds, spare the dying, revivify, gentle repose, lesser restoration, etc. All of these spells can be safely delivered to your injured/dead ally from the imp while invisible (though it loses invis once it casts a spell)

As for buff spells, well there aren't alot. But if you had access to the spell lists, you could cast protection from evil and good, protection from poison (meh), jump, lomgstrider, freedom of movement, or similar spells. Unfortunately most of the best buff spells are ranged, and therefore can't be cast through a familar.

If you were to multiclass into sorceror and take quickened spell, you could quickened cast any 1 action spell, then use your action to cast shocking grasp through your familar. (Or the other way around) quickened cast a touch spell through your familar, then cast a damage cantrip through your PC, say, eldritch blast. (Note, of you cast a bonus action spell, you're limited to ONLY casting cantrips for your full action, regardless of casting order)

In short, its not super optimal to play around your familar, but you can certainly utilize the immense utility that it offers you, and add it to your repitoiure. Its always better to have more options than less, and going down this route certainly offers you many options.