Lightweight long sleeved clothes, and a uv/bugscreen shade for your stroller. You won't find a "chemical free" sunscreen or bug-repellent. That's like trying to find water-free juice. It is the chemicals that make them work, even in natural products based formulas. We cheated and used sunscreen early, but avoided parts she tended to put in her mouth. we have a family full of fair skinned sunburn prone people, of which she is included. I like the Aveeno baby sunscreen, and the Off Family care unscented bug repellent (it has DEET, but if you are going to be outside with ticks, large mosquito populations, etc, you really do need it to be effective).
FYI - another poster said Skin-so-soft has DEET. That is only half-true. Original Skin-So-Soft does NOT have DEET, but it also doesn't really work (especially against ticks, etc). Skin-so-soft Bug guard does have DEET. It is a traditional insect repellent.