Hey Rob, just noticing your user name. Are you the Rob Twohy that converts D&D books and modules to Fantasy Grounds? If so, I know and admire your work, and extend my thanks on your efforts. Most of the content I've played on Fantasy Grounds has been stuff you converted, and picking your modules apart and seeing how they are made taught me a lot with regard to designing/converting modules.
Once you feel ready to move on from Starter Kit to full ASL, you will need the Rulebook (ASLRB), and the module Beyond Valor. That will give you the rules, informational and system counters, and German and Russian units. It will also give you several more mapboards with lots of scenarios to play on them.
There is Solitaire ASL (or SASL) but that is only for full ASL, not SK. To play this you will need the stuff I just mentioned (ASLRB and BV) at a minimum, but SASL can always benefit from additional modules, as SASL uses randomly generated map configurations and all mapboards in your collection are eligible.
Beyond that, each core module adds one or more nationalities, as well as new mapboards and scenarios. Yanks, which adds the US order of battle unsurprisingly, also includes Chapter E pages for your rules binder. Chapter E is basically a collection of special rules that are not used in most scenarios, but are necessary for certain scenarios. Stuff like airdrops, glider landings, weather effects, night combat, skis, assault boats, creeping barrages are found in Chapter E. Lots of cool stuff in Chapter E.
There are also what we call HASLs, or Historical ASL modules. These focus on a presenting a specific small battle or section of a larger battle in much greater details. These include 2 innovations, both of which have helped HASLs to become enormously popular among players. The first is historical map of the terrain presented on a large paper map, as opposed to generic terrain mapboards. Charlie Kibler's map for the very first HASL, Red Barricades, was a jawdropper. I doubt there is any ASLer who didn't want to play a game on that map when they first saw it. The second innovation is the Campaign Game (or CG). Instead of just a single scenario simulating mere minutes of time, the CG allows fighting that continues over days, or even weeks. Force preservation is suddenly maximally important, and the player can spend points each day to buy reinforcement groups, giving small packets of infantry, guns, vehicles, or artillery or air support to add to their forces.
Just a brief overview of what you might like to take a look at after getting your feet wet with Starter Kit.