If you don't want sheeting, you don't need it, but you do need something to prevent wing twisting. If you look around, you might be able to find some of the older plans that show a wing with no sheeting but with 2-3 small spars between the main spar and the LE of the wing. If I recall, the origional PT-40 uses this construction. Also, the Golberg Eaglet is a .25 size trainer with no LE sheeting and only a LE, top, bottom, and TE if I recall. It does have a sheeted center section though. (I built one about 12yrs ago, so the design might have changed since then, I haven't seen one in a while). We flew that Eaglet pretty fast at times and never noticed a twisting problem. You'll want shearwebs, of course. You might consider doing the webs front and back rather than betweent he spars to create a "box spar" type thing. You get more glueing surface area compared to the edge of the sheeting.

As mentioned, you'll want sheeting on the center section, that's where the flight loads are highest.

As a side note, one advantage of LE sheeting is that it forms a more accurate airfoil compared to covering over an open structure. Depending on what kind of flying you're doing that might or might not be important. For a .25 size plane, you can use very light 1/16" LE sheeting to keep weight down.

I also agree that hardwood spars would be overkill. You'd be fine with balsa of a reasonable size, and lighter in the end. Just use fairly hard balsa for the spars.

You'll want a stearable nosewheel, but you can get away with out the rudder if you really want to. However, on the whole, I think you'll be happier in the long run with both rudder and nosewheel.

If you want to save weight, go with a tail dragger, a hitech HS-85 servo will work on a .25 size rudder (unless you are 3Ding), and will weigh less than a nose strut and wheel anyway.

Lots and lots of options. Have fun