If you like working with wood you can also get Basswood in many of the same precut shapes and sizes as Balsa. Basswood is a bit firmer with a less prominant grain. Pine is available from most hardware / lumber stores in useful sizes for larger projects (1x1, 2x2 etc) some of the molding trim is handy as well. Even better for hobby use many of these shops keep a scrap bin where you can get short remnant pieces cheap, 2 feet of trim is pretty useless for them but can supply us with enough for several projects. Pine is soft with a fairly tight grain.
If you put a coat of shellac over the wood and sand it before you paint it will reduce a lot of the wood grain effect from wood. You can use clear shellac or white BIN primer, both work well.
There is a member here Solid who has done some really neat all wood aircraft. I believe he uses Mohogany for most of his work.
Getting away from wood there are a couple of epoxy putties that are pretty handy. I use Magic Sculpt, but there are others out there I just can't think of the brand names at the moment.