Toni,

I can completely relate to your plight! I live in a house that was built in the 1920's and it also has the same type of indentations. At least in my house it's from plaster walls. I have chosen to leave them plaster due to the fact that they can be painted (I just can reccomend high enough the idea of using the thickest nap possible on your roller and expect to need more paint than on a flat wall) and I have painted a few of mine.

As for the idea of flattening them yourself, you most certainly can do it though I reccomend using a joint compound instead of a spackle for at least 2 reasons. 1)You can buy it in large quantities and it will cost you much less 2)It's made for this type of use and you can thin it out to the perfect consistency and possibly even roll it onto the wall once you have gotten it pretty smooth to create a type of orange peel texture.

In regards to both your ceiling and walls, while I would love to say that you'll be able to make them perfectly flat, I'm sure by the time you finish working on them you might have the technique down though it is very technique sensitive. All I'm trying to say is don't expect to do it perfect the first time. So instead look at a few different techniques that will help to hide any left over imperfections, such as orange peel or knock down. The best part is that some of these techniques like knock down will make your house look like it is new construction. (In case you are wondering what knock down or skip trough, similar techniques, this is where you apply a certain type of texture to the surface and then flatten parts of it, allowing some of the texture to still show through.) Hope this helps!