As stated above, you can use a good bunch of Landsknechts in many armies of the perios, in this outfit roughly from 1500-1550.
Some epic battles were Marignano (the French, using some 15.000 Landsknechts beside their knights and artillery, vs. the Swiss), Ravenna (Spanish and Italians vs. French with lots of Landsknechts), Bicocca (French with Swiss vs. Imperials with Spanish and Landsknechts) or Pavia (French with Landsknechts and Swiss vs. Imperials with Landsknechts and Swiss). The Ottoman assault upon 1529 was decided in a large breach between Janissaries and Landsknechts, too, and when Suleyman returned in 1532 with a larger army Charles assembled an army of some 120.000 near Vienna – the largest battle of its time that did not happen. On the other side, Charles conquered Tunis in 35 and failed before Algier in 41. Landsknechts were the staple of most German conflicts, eg the siege of Münster, or the religious war that Charles won militarily while losing politically.
So, in short, pick your favourite opponents and build the army around your core of infantry. From Spain to Sweden, from English usurpers to Poland or Hungary you can put a good bunch of infantry in the center. Just don't build them with crossbows. Landsknechts used the pike (~80-90%) with some heavy weapons thrown in, the rest used arquebus. Similar outfits would be worn with the artillery, though de jure they were not part of the Landsknechts.
Depending on the army you play you will definitely want Gensdarmes, light cavalry (eg. Stradiots) and light infantry (Italian or Spanish arquebus, French crossbow & arquebus) to complement them. Swiss were most often on the other side (and there was usually no quarter between them and the Landsknechts, as a heritage to the Swabian wars, though the Swiss had a habit of taking no prisoners regardless of who the opponent was).
In summary, who will they NOT fight. French, Italians, Spanish/Imperials, Ottomans, Russian, Polish, Swedes, English and, of course, all versions of German forces with other Landsknechts at their core – OK, afaik they did not fight the Scots, so avoid these for now.