Okay, "from first principles" means "graduate-level mathematics, and beyond, being stuff with which the 'great minds' of mathematics have had trouble". "Beginning with Algebra 1" means "middle- or high-school algebra, and onwards" to some point, possible undergraduate college. So these are two very different things.
If you have no training since high school, so your "foundation" is whatever you can remember from that, then you might want to consider starting with the algebra. Then study trig, maybe some geometry, and then calculus. Throw in some linear algebra, and definitely take a class on "foundations of mathematics" or "proof theory" or some such course. Then you can think about diving into "first principles", such as building the natural numbers from the empty set, the set containing the empty set, the set containing the empty set plus the previous set, etc. (It'll get really weird, really fast.)
Have fun!