This is a horse that will never die.
Your sound is the sum of everything that happens between your fingers and your speaker cabinet and beyond. A pedal by itself has no sound at all. It receives whatever you send to it and spits out however it's altered, either by merely passing through the pedal circuit, or however you turn the knobs. Where you put that pedal in relation to everything else can produce profoundly different results. I think one of the best resources for understanding pedals and tone is, without doubt, the "That Pedal Show" channel on YouTube with Dan and Mick. If you've never seen it, let me apologize in advance for how many hours you will donate to binge-watching their episodes. I've learned a ton from watching them and putting their lessons into use.
Here's an episode with Josh Scott from JHS Pedals about the different gain pedal types out there.
Wampler is also a tone genius and makes wonderful products. The PlexiDrive is sensational.
You should probably plan to own several pedals of different types to discover what you're looking for. But in terms of overdrive, one of the most iconic and permanent pedals in the overdrive universe is the Ibanez Tube Screamer. They make a vintage reissue version that is so excellent, I have two of them. Also, RYRA (Rock Your Repaired Amp) makes an incredible KLON type pedal called the Klone. It is pure rock and roll. I can also second the Paisley Drive, it's an excellent, upgraded TS type pedal with excellent drive. Perhaps the pedal in my mind that covers literally every possible base (and offers 299 MIDI presets!) is the Strymon Sunset. It has two sides with individual tone stacks that combine in incredible ways. Given the real estate that pedal covers, I'm not sure you could do better for $299.
Have fun!