My front flower bed is mix of annuals, biennials, and perennials.

I reseed some more every spring. Not everything survives but enough does to make it a nice little mass of color. I have had some perennials/biennials remain dormant for an entire year and germinate the next one.

It's completely overcrowded mess where there's always a few weeds that nobody sees.

You can certainly mix them, and in fact a lot of seed mixes already have both. But the ideal seeding season is late summer/early fall, at least in my area, since that's when existing plants drop their seed to be buried through the winter and sprout in the spring. Hopefully your plot is not too big, because you'll probably want to be pulling weeds while the flowers get started. That's what I'm resigned to doing once the last frost is gone since I missed seeding in the fall.

Much depends on where you live. Annuals require more water than perennials, so it's not advisable where I live.