Flux spattering is not uncommon and if you're right up close it could spatter in your eye. Fumes are not so much a concern for eyes- more for breathing- and flux fumes, not lead (if you're even using lead-based solder). It's possible that you could get actual solder spattering in some kind of rare situation (trapped liquid or something) but it's very, very rare under normal conditions.
Since the splashes are tiny, existing eyeglasses, drugstore reading glasses or "Home Depot" (hardware/home improvement store) glasses work fine. Price range might be $2 and up.
The ideal kind might be the wrap around type. You can find various types here, for example:
Home Depot USA (in USD)
Home Depot Canada (in CAD)
If you're soldering small parts under a microscope you usually don't require safety glasses, but the objective lens may be protected with a transparent shield.