Both the Honda Civic and Mazda 3 are more sporty than a Toyota Corolla, no question. Both are also fairly reliable as well. The 2016 remodel of the Civic was not troublefree as they made many chnages to the car and there have been reports of fuel pump issues, climate system issues, and some electrical issues. Consumer Reports notes it as well over those years. Older cars (pre 2016) are stellar in reliabilty in comparison with no real trouble spots at all. So if you go 2013-2015 which is also in your price range you should do pretty well.
Regarding the Mazda 3, it is the most sporty of the japanese brands. There is a reason their old comercials were "Zoom Zoom" and it has to do with their handling and responsiveness. From 2011 to 2013 there were few problems but they are pretty old. Another redeisgn in 2014 caused some drive system (transmission) issues so avoid that one year. However from 2015 to 2018 they are solid cars as well. Some have electronics issues but besides that they are very reliable.
So if you want an older car, I would go with the Civic on reliablity - newer, the Mazda. Both brands for those years are in your price range so it depends on what you want - but I would focus on 2013-2015 for the Honda and 2015 to 2018 on the Mazda (I know the newer ones are probably out of your price range, but 2015-2016 probably would work for you).
Best of luck.