Brass is certainly a possible alternative for making small spars. Styrene is a lousy material for small spars; the same attributes of flexibility that made it excellent for hull planking pretty effectively rule it out for spars.
At the risk of sounding blunt, if a wood spar is flimsy it’s because it’s made out of the wrong kind of wood. Basswood is out of the question; too soft. I think I can say that few serious modern modelers like oak. (Too splintery, and the grain is way out of scale.)
The woods that, I think it can be said, veteran American ship modelers like best are boxwood, pear, holly, and cherry. Unfortunately all of them are pretty hard to find (with the possible exception of cherry). Those are all hard, stiff woods that take a nice finish and won’t bend significantly under the strain of the rigging.
For my models of H.M.S. Bounty ( http://cs.finescale.com/fsm/modeling_subjects/f/7/t/155394.aspx?sort=ASC&pi240=1 ) and the Continental frigate Hancock ( http://cs.finescale.com/fsm/modeling_subjects/f/7/t/155391.aspx?sort=ASC&pi240=1 ), I turned the spars out of degama (aka lancewood). It’s an extremely dense hardwood that refuses to bend. (It is, however, willing to break. I found that out the hard way several times.) I used my dear old Unimat SL lathe; for the first few passes I used a metal-cutting tool bit in the cross-slide to get the stick down to about 1/8", and fine sandpaper for the rest of the job. Some of those spars taper to well under 1/32" in diameter.
Whatever material you use, it’s extremely important to get the taper right. David Steel’s Elements of Rigging and Seamanship, or James Lees’s more modern The Masting and Rigging of English Ships of War, 1620-1860, will show you the rules.
Unfortunately the dealer from whom I bought the degama went out of business about 35 years ago; I have no idea where to get that species today. For my last wood-sparred model (the Model Shipways Phantom) I used cherry. Woodworking supply companies sell cherry dowels down to 1/4" in diameter. It’s a little dark to be ideal, but really nice stuff to work with.
Hobby shops and places like Lowe’s sell dowels in three species: oak, maple, and birch. Of those, I vote for birch. For years I’ve read stories about birch warping, but I’ve been using it for a long time and have never found that to be a problem. Maple is good stuff too, though pretty brittle. As I mentioned earlier, I don’t recommend oak. Unfortunately the dealers often don’t specify which species of dowel is in a bin. Birch and maple can be hard to tell apart.
Model Shipways says the dowels in its kits are beach, but I have yet to buy one with spars made of anything but birch.
Hope that helps a little. I know I’ve expressed some rather strong personal opinions; take them for what they’re worth.