This depends on whether you just want to put up drywall, or insulate as well. You're never going to have a better chance to do the latter.
Per This Old House, if you just want drywall or paneling, the best approach for a full-height wall may be to affix horizontal 1x2's to the wall using some mixture of concrete fasteners and modern construction adhesive, then screw 1x2's vertically to those on standard 16" to 24" centers to act as the "studs" which the wallboard is fastened to. The advantage of having two 1" (nominal) layers is that it gives you clear paths to run wiring either now or later. This is nonstructural so you don't need a header or footer, though fire codes may want you to seal the gaps at top and bottom with foam or leftover construction adhesive.
If you want to insulate, you have several options. One is to use deeper wall construction which has space to contain insulation; details depend on the kind of insulation you want to use. As an alternative, there are insulation products which have plastic studs built into them so you can just glue them to the wall, screw the wallboard directly to them, seal top and bottom (again), and be done. This works nicely on concrete foundation walls, less so on other construction; see the manufacturers' websites for details. These have wiring channels designed into them so you don't need to plan for that. Cost was roughly comparable when I did my own basement. (I used InSoFast and was generally happy with the product and customer support; I have no affiliation with the company and there may be others just as good or better.)
Note that in your case, since there is a "real" (hopefully insulated) wall above that step, you may not need all of this complexity. If your wiring can run through the framed upper walk, the bottom section can ignore that issue and just be cosmetic and, if desired, insulating. Putting a board on top to cap it and join it to the framed wall is perfectly reasonable, though you may need to scribe and trim that to match the walls shape unless you can slide it under the upper wallboard. (Nothing in a house is ever perfectly plumb, square, or straight.)
One possibly useful trick: I stopped the wallboard two inches above the floor, and used pressure treated 1x4's as baseboards; that gives me a bit of a buffer against any water that finds it's way in being wicked up into the wallboard. Also, I used gypsum board rather than plaster board, for the same reasons gypsum is recommended behind shower enclosures: it's inherently more resistant to water and mold. (I considered using fancier materials but decided this should be more than good enough.)