Vegetable Oil in cakes and / or food? What type?

I agree with SCP. Safflower is the mildest/most neutral flavored oil in my experience. This is my first choice in baking. In anything chocolate, I always sub a portion of the oil for coconut oil. It enhances the flavor of chocolate and makes baked goods richer in much the same way as butter.

I personally use a super mild olive oil in all my baking. If I don't have that, my second choice is safflower which is an excellent substitute and is the lightest and mildest of all. Coconut oil is great, the more refined the oil the less coconut flavor it has (in other words, don't use extra virgin cold pressed if you don't want coconut flavor). As for grapeseed, I have a sensitivity to it so I can't stand the flavor and it makes my tongue burn (in a similar way to other strong oils such as walnut or pecan). But maybe that is just me. If you are looking to go "organic/natural" stay away from canola, canola is a GMO product.

I substitute applesauce for half the oil. Works great. Any good quality tasteless oil can be used.

I'm a big fan of Spectrum's organic oils and use their canola oil and coconut oil for baking, and their extra virgin olive oil for cooking.

You also asked about what to use for savory foods. Without a doubt extra virgin olive oil. Brand and quality make a huge difference I'm taste. I prefer colavita

Coconut oil adds amazing flavor

There is cheap oil, usually soy oil, labeled "Vegetable Oil,' but grapeseed and organic (which must be non-GMO) canola oil is usually a better quality.
When you are using substantial amounts of oil, as in some cakes, I believe you can substitute applesauce (or plum/prune butter) for part of it, but not oil, as it has structural roles to play.

Great! Thanks again! Brilliant response!

For brands, I use Wesson's Canola Oil or sometimes Crisco's Canola Oil. If you shop at Whole Foods, try and get "Expeller Pressed" Canola oil. This type is considered better by many because the oil is extracted though heat and mechanical pressing, rather than chemically extracted. Also, non-expeller pressed Canola Oil can leach trans fats when heated for frying or in baking.

Vegetable Oil, just Vegetable Oil, will work fine for mo(i)st cakes. Canola oil is slightly healthier. And Grapeseed Oil will work fine. Basically any oil that does not have a distinct taste will work in cakes.

Maybe Kelsey will weigh in but if you don't want to use canola oil you can use grapeseed oil. I use oil all the time in cakes and find that a neutral flavored oil works best. I usually use canola.