I rode nothing but freewheel bikes from 1970 until 2005. Never broke and axle, but I bent a couple, especially when using Normandy hubs. These were all with 120 and 126 mm hub spacing. If yours is 130 mm or wider, then yeah, a freehub wheel might be a better idea. But I've replaced many broken axles on inexpensive hybrids and never had one come back. The trick is to make sure the drive-side locknut is good and TIGHT. And just to be safe, check the wheel for wobble once in a fortnight or two.
And yeah, you can order axle-cone-locknut sets directly from wheelsmfg.com, or if you're unsteady about taking things apart and measuring, your local bike shop can measure and order for you.