>>3095217I'd say, take a look at the Panasonic LX100. Small, discreet, fast af, fast lens with a nice range, good battery life, good video and a great UI/UX made for enthusiasts. IQ is fairly good as well, though only 12Mpx, but that should be enough if know what you're doing. The evf is kind of crap, but gets the job done. I got mine for 500€ used a while ago.
X100t is good but has very limiting fov. X-Pro 1 is too old and sluggish to be any fun and doesn't want to focus the 35/1.4. Don't listen to faggots like
>>3095221, 35/1.4 is a good lens and focuses fast enough on the better bodies like the x-t1, but the new 35/2 is much better. Fast af and sharp as all fuck. The cheaper bodies like the x-e2 could be worth a look, but in all honesty, Fuji is an expensive system to get into, I would not recommend if your budget is limited.
a6000 has a good sensor, but I find the terrible UI/UX extremely off putting, and the e-mount lens ecosystem is going nowhere. You could get it with the cheap sigma trio and stay in your budget, but try it out first. I've had the 30/2.8 sigma and it was sort of disgusting to use. It felt like it could break any time.
Then again, you could sell just your 600D and get something a bit more fresh. There is no point changing systems just because.