Basically set up like 64, but larger levels, and more branching paths.
Plot-wise, I'd like a reboot...like basically the plot of Star Fox 64. However, I wouldn't mind them adding Krystal (rewriting her story) to appease the newer fans and to have a female character. And keep Pigma as a loose-cannon and Panther among the Star Wolf squad, as he was pretty cool.
Graphics should go for the "puppet" look of the old ads, except a little more appealing, with the cut-scenes being really corny and paying homage to classic Sci-Fi films and such, like how 64 did with Independence Day and such.
Get some decent voice-actors, like Wonderful 101 and Fire Emblem and Kid Icarus did, maybe that same group?
Finally, go for a good Wii U GamePad integration, like make it the cockpit and allow you to quickly see what the other characters are up to, give them orders, talk to them, etc. with a quick tap of the finer.
Also, I think it'd be cool if the Arwings could morph into mechas for the "ALL RANGE MODE!" fights.