I've repeatedly made the case for something similar. But I don't think the argument should be "Taking care of yourself, in any case, yields better outcome, even for others, than prioritizing the common good. So the fundamental principle should be putting yourself first.". First, it's not always true that taking care of yourself is always the best -- sacrifice does exist and is important.
If you as say a father always put your own wellbeing (or some other definition of self-interest) first, then you're going to be a pretty lousy father. But you shouldn't ignore yourself. It's all about striking a balance, and in the end this balance simply aims toward the common good.
It doesn't make sense to say that because sometimes a naive, "greedy" strive toward the common good doesn't work then the principle is false.
You can carve real basis for the common good and other metaphysical principles. One such basis is that, metaphysically, the supreme valuation of the self is on very shaky ground. The self, although very important conceptually, doesn't stand up as an ultimate metaphysical basis, because we are really dynamic results of a whole network of interactions that includes not only whatever happens in our brains, but the whole cosmos -- there's no absolute boundary between yourself and others, and everything is always fundamentally changing. You from today is different from yesterday, and significantly different from many years ago. The common good is much more metaphysically defensible. That's why most metaphysical traditions (religions, usually) almost universally put the common good (sometimes enacted by God) above all else -- it really makes the most sense imo[1]. Again, you shouldn't be naive about it, and in practice and in most cases it makes sense to first take basic care of yourself, "keeping your house", and then go help others, but this is more a guideline, heuristic and reminder (specially important to give for radical altruists, but common sense for most people I think).
But really if yourself is your actual fundamental priority, I think you will act very poorly. Although even in that case there are good strategic reasons to be cooperative (people thinking you are evil or egoistical will already turn around many people and compromise relationships and cooperation opportunities).
[1] If you don't buy this metaphysical formulation, there's an (I believe) ultimately equivalent formulation that may be easier to accept: the fact that you "Could exist/could have been born as another person". If in some metaphysical sense you could have been born as that poor person that needs assistance, doesn't it make sense to help her, which logically implies that if you were in their shoes you would be helped?