Missed the magic bit - what you have for an amp. Max that out, then go pedal shopping, or amp shopping. Young ones using a 10w peanut practice amp that has a sucky tone can jack in a $1000 guitar through ten pedals, and still have a sucky tone. You got the ball.
Past that, if you have a good amp, many working club players will prefer a DSP/multi-effects pedal. Learn its programming (not simple), cable-up, and 'rockin'. If, however, it goes down, it's all gone.
UPDATE: Next day, with a little support? I'm just sayin' if you have an 'elcheepo amp like a Fender Frontman, or something worse like a no-name from Walmart, that's the thing to go after. There are decent small/small wattage "modeling" amps for around $150 that, in "effect" have enough on-board effects to be pretty cool. The other thing is that floor pedals and the switches on them tend to break pretty easy. Your foot isn't as gentle as your hand, thus the name "stomp boxes".
Then you also haven't indicated what kind of tone you're after. I like fat/hot/bluesy/tube-overdrive, but others want serious distortion, reverb, echo, etc. The only pedal always on the floor here is a compressor/sustainer, but I got some nice amps. If I was headed for a jam and didn't take an amp, then it would be a Tube Screamer carried in the guitar case, just in case.
Got lotsa pedals I don't use anymore. On stage, reverb, phase, flange, and echo tended to weaken my punch and definition, so got left in the gig box more and more. Sometimes less is more.
UPDATE 2, per your comment: I really, really wish I knew what amp you have, as you may not be tuning it in to it's best "fat". Or it can't ever get fat. Whatever. Remembering the piles of amps & pedals I've used over the years, I'm thinking there ain't much in pedals that will make a fat tone, more likely thin it while pursuing the God of Tone. Going sideways, gimme 40+ watts and a 12" speaker (or two), 'fat city. With enough punch there, it's magic to start using the neck pickup and let that thin bite-yo-butt bridge pickup go for a change.