It's generally best to fill with the same material as the finish, but that's not always possible. In this case, where the finish is nitro, that's the way I'd go given a choice.
Any time you get a dent that is simply compressed it's best to try to swell it out as soon as possible. The longer it sits there dented the more it 'gets used to' it, and the harder it is to swell out. Another big advantage of immediate action is that there's less chance that you'll get dirt in it, which can be difficult to clean out.
Most finishes are at least resistant to penetration by water; that's one of the functions of the finish. Nitro is brittle enough that it often cracks microscopically when it gets dinged and that admits some moisture. Thin finishes can be more easily penetrated than thicker ones, even if they're not cracked. Try putting some clean water over the dings and letting it sit for a while. Then warm up the area carefully with a hair dryer. Some finishes, such as shellac/FP will craze when heated, and the wood may have been sealed with shellac. Also, lacquers vary, so watch it closely! With any luck you can drive some moisture in through the finish with the heat; if so the wood will swell a bit. Often it's helpful to heat the surface until the water all dries off, and then, while it's still warm, put on some more and repeat. Even with the wood swelled up the dings may still be visible, but as the moisture dries out they should lessen. This may take a day or so.
If the wood fibers have been broken you will never get the ding to go away without surgery. Patching something like that in so that it's no longer obvious is one of the trickier aspects of repair, and you'll need to practice on something that you don't care about for some time to learn. You can fill it level with finish, but the actual damage will still be visible. Filled dings like that are in the category of 'clean dirt'; honest wear that shows the guitar is not simply a decorative wall hanging. So long as it's your guitar that's honorable. It's another story if you're trying to sell it as 'new'. Any maker can supply you with horror stories on that score.