It depends on how Nintendo plans to release the game. If it's DD only, I'd like something similar to Starfox 64 with linear levels and multiple path.
If they choose to release it on a disc, then I want an improved Star Fox Command. Command was bad because of the ridiculous story and the lack of linear levels, but they can definitely improve on the strategic aspect of the game. They have 2 solid tactical licences (Advance Wars and Fire Emblem), so they know their stuff. It's not like they can't put linear levels here and there in the campaign. It would be nice to have an arcade mode to supplement the main campaign mode too. I tend to get bored of the old Starfox after 30 minutes or so, so maybe they could make a smaller game that focus heavily on making high scores.
People hate Starfox Command, but I don't think the Command aspect was to blame, it was a pretty neat idea, but the game had its share of problem, like the stylus gameplay due to the lack of analog stick, the stupid and pointless cut scenes/story, the lack of variety. But I have the same problem of repetitiveness with the old Starfox, and the command aspect made the DS game finally enjoyable to me, to this day, it's the only Starfox game I ever finished, I always get bored always, the lack of checkpoint/save system didn't help though.
I wouldn't mind another attempt at third person shooting, especially if a western developper like Retro Studio is developping the game, but if it's from Japan, they'd better stick to vehicles...