Physical sunscreen ingredients like zinc oxide and titanium dioxide are great because they protect from both UVA and UVB rays, but because they're literally a physical barrier from the sun, they leave a white cast. If you want to avoid that, your best bet is to find a sunscreen with Avobenzone, or basically anything that ends in "benzone". Avobenzone is a chemical sunscreen that protects from UVA rays without leaving a white cast. The SPF number on the bottle is an indication of the protection from UVB rays, but that doesn't necessarily mean it protects from UVA rays, the rays that cause aging, so make sure to check the ingredients.
If you're looking for something for oily skin, try looking for words like fluid or liquid. These are less likely to contain ingredients that will make your skin feel oilier. Also, waterproof sunscreens tend to be a bit less oily since they're formulated not to rub off or wear away easily, so you might want to look out for that. I know for a fact Neutrogena has a high spf liquid sunscreen, and Murad apparently also has one, so those might be worth checking out.