My in-laws have a 3 season porch. It gets used very frequently. I've also seen a ton of 3 and 4 season rooms while casually house-hunting on Zillow this year.
The top #1 absolute must-have if it were me would be some kind of fireplace/stove. Wood stove would be most ideal but at the very least, a gas fireplace for the kids to huddle in front of on a cold winter day and watch the snow fall while coloring/reading.
Electrical outlets spaced appropriately would also be ideal - one bummer thing about the in-laws' setup is that there are too few electrical outlets.
A high end ceiling fan that can move a lot of air is also up there for me.
What kind of windows/screens will you be installing? I think if you could have as many windows 'open' in the summer and closed in the winter, you'd be able to best maximize the use of the weather.
My in-laws have outdoor furniture, and one of the couches (wicker/metal frame) folds out into a bed. On a cool summer/autumn night, nothing beats sleeping with a fresh breeze rolling through the room.
In my personal screened in porch, the floor would be carpet - obviously the type designed for porches but also not astroturf. That being said, my in-laws have teak slotted floor "tiles" (similar to
these ) directly over the slab on the porch, and then in the sitting area there's a nicer weather-resistant area rug over them.
Ultimately, though, it would really depend on just how you plan to use the space. I think a sound system is a really good idea but these days, bluetooth speakers are more than adequate and less likely to be obsolete in 10 years.