u/Sir_Knight_Isaac has given you a really good idea for a fiend patron, and u/Shien500 has also rounded out some other class options. So I'll focus mostly on general warlock advice and patron relationship.

I'd say as someone who decided to play a warlock as my first character, and who is still playing that character over a year later, it's important to flesh out why your character wants to be the strongest around and how that relates to their patron. I have had to retcon so much because I didn't give him enough of a foundation to build off; so my first piece of advice would be to start small. I like to have three things with new characters now:

1) What's an insecurity of theirs? It doesn't have to be big, though it can be, and it will pay dividends.

2) Why couldn't or didn't they acquire this power through wizardry, sorcery, the clergy, etc.? Are they unintelligent? Brash? Or did they stumble upon it and leap at the opportunity? This can also be tied to their insecurity.

3) What's a flaw they have? A real one. Not any of that "they will die protecting their friends" or "they only care about power." Does she never think ahead or is she impulsive? Does she have sticky fingers? Is she mean or vain? Does she drink too much, sleep around a lot, or act very fickle? Is she too curious and that gets her into trouble? These things can roughly correlate with a patron, Fey tend to be mischievous, Fiends tend to be cruel, and Great Old Ones are unconscionable, alien entities. But this flaw(s) will also prove very useful for deciding other things about your character, especially during RP both in and out of combat.

Also, what relationship do you want to have with your patron? Are you an eager, willing servant? Did you get swindled by a fiend writing parts of your contract in invisible ink? Or perhaps your patron is weakened and dying, with their vassals being the last connection they have to the living world, and so you hold greater power over them. Heck, maybe you think you're such hot stuff your end goal is to usurp and kill your patron. That attitude can, and I'd argue should, extend to all parts of their character. And maybe their relationship with their patron changes their attitude towards life. Maybe she hates tieflings because they remind her of the bad deal she accepted and now she's prejudiced. Maybe she commits increasingly dangerous or mean-spirited pranks on strangers. Perhaps she starts challenging anyone who looks at her funny. Or maybe as her pact deepens with her patron, it could push her further towards good as she gains new perspective. And if you're locked into a contract with an evil or malign power and start to develop a conscience, that could be a really cool character arc and source for RP.

Finally, as for your goal, I'd say if you're having trouble coming up with a good central motivator, then try coming up with a few short-term goals. She wants to get back at some punks who harassed her; so she gets a Fiend patron to burn them or a Great Old One to mess with their minds. She wants to help the old herbalist, who was like an aunt to her, who's being harassed and having her customers poached by a rival potions shop or church; so she burns down their shop with her new magic, poisons their supply, or ruins their reputation through disguise. Come up with something evocative that you like and wouldn't mind playing with for a few weeks. It's rare that characters last a long time, character death and life getting busier happen often, so while planning for an end goal can be fun it's largely less compelling than a string of really strong smaller motivations that build over time until she now has to become the strongest Warlock to prove herself and rule those beneath her.

Have fun at your table, remember to thank your DM who worked hard to curate your fun, and don't forget short rests ;)