You really can't go wrong with any of the cars you mention; all three are great cars, but there are significant differences.
Both Mazda 3 & Mazda 6 are fun to drive cars with excellent overall reputations. The M6 is a sleeper and has not sold well in the US so it will be harder to find. But, thanks to its sleep status, will probably cost less than similary equipped M3. A quick search for model years 2014 through 2016 in Seattle area shows 10 M6s priced under $13K vs 26 M3s. So the selection of M3 is significantly better.
Aside from price, I'd say it boils down to your size and comfort preferences. The M6 being is larger and will be more comfy. The M3, being smaller, will be more sporty but a bit rougher in the comfort category.
The Honda Accord is perannually a well made favorite of many and a notch better overall than a Mazda. It will be larger and more refined that either Mazda and due to its popularity, will cost more. To get a similarly equipped and priced Accord vs a M6 you would probably have get a year older, higher mileage Accord.
We always appreciate hearing what you end up with and why. Happy car hunting!