By strategy, if you want something more actiony/real time then the Codename Panzers series (Both Phase One and Phase Two are available on GOG) are fun and fast paced. They do not have base building or anything like that but they allow you to command a decent number of soldiers and a wide variety of vehicles (Firefly Shermans, Stuarts, normal M4 medium tanks, Panzers II, III of a few varieties, and at least one of IV and V as well as Tiger tanks, Soviet T-34s and T-34 85s as well as Katyusha rocket trucks, among many others). The damage model is somewhat realistic with armor being displayed in sections which are damaged individually even though the vehicles do have their own overall health which will go down with every attack. Unlike Company of Heroes I do not recall machine guns uselessly attacking enemy tanks they cannot damage.
https://www.gog.com/en/game/codename_panzers_phase_two https://www.gog.com/en/game/codename_panzers_phase_one Next is the Blitzkrieg series. Even though the people at Nival lied and never let us get Blitzkrieg 3 the first two games and their expansion packs (okay, Blitzkrieg 2's X-packs are harder than nails) are some of the best strategy/tactics games set in World War II. The command depth in both these games are pretty good without being too detailed but they are slightly better in the first game. Your infantry are more expendable in the second game as well but you also get core units in both games along with other units given out on a mission by mission basis. Those core units gain experience and can be upgraded. For instance you might start with some heavily armored cars as the British in Blitzkrieg one but end the game with Pershings or Easy Eights. These games have a really wide variety of units and vehicles which nearly dwarfs the amount in Codename Panzers. You have infantry assault squads equipped mostly appropriately for different era of the war (like 1941 vs 1945 where in 1941 your dudes might have just Springfield 1903's but in 1945 they have an M1919, M1 Rifles, M1 Carbines with silencers, or M3 Submachine guns for the Americans). Blitzkrieg 2 has a fun mechanic where you get a number of reinforcement points which you can use them entirely in a given mission or carry them over as best as you can into the final campaign mission. I love all of the games mentioned above very much.
https://www.gog.com/en/game/blitzkrieg_2_anthology https://www.gog.com/en/game/blitzkrieg_anthology Men of War series starts on this website (in English anyway) with Soldiers: Heroes of WWII and then moves to Faces of War. After that the games are called Men of War. If I had to recommend just one of these games I would recommend either the first game or Assault Squad. The first game called Men of War is a very good game for a lot of things but many of the missions inside operate somewhat like "Soviet Commandos" (that is like the Commandos games but from former Soviet countries). You almost need to view the soldiers as lives to accomplish objectives for the stealth missions. The German campaign is probably the best one from a mission design standpoint. They are generally more tactical or strategic rather than many of the Soviet or Allies missions where you have to sneak around behind enemy lines. Also, lots of the missions are in the African theatre. I found out later that in Russia this game is called Behind Enemy Lines 2: the Desert Fox.
Assault Squad has no base building but has linear (as in triangular maps) levels with static objective points. It's kind of like Battlefield meets Men of War, is a way. This is an appreciably more casual game to play with few stealth oriented missions and of those none are obnoxiously impossible. The weapon depth and vehicle variety is astounding in these games, either one, but Assault Squad is a little better in the base game. I find the lack of particular advantage to the M1 rifle in the first game kind of annoying but this is fixed with a faster rate of fire for semi automatic weapons in Assault Squad. Also, tons of obscure weapons appear in Assault Squad like the Johnson Rifle and some off the wall Japanese sub machine gun that the special forces get (I am sorry, I do not remember what it is called).
If you see a men of war game you would like to try first, then if you feel the need play whichever one looks best to you but I would ask that you first try either Soldiers or Faces. Faces especially is a harder sell after playing Men of War. Also, I thought those two games were not as good as any of the Men of War games and the only reason I played through them was because I love WWII games. Soldiers especially comes across like Soviet Commandos with all the actual commando raids.
https://www.gog.com/en/game/soldiers_heroes_of_world_war_ii https://www.gog.com/en/game/faces_of_war https://www.gog.com/en/game/men_of_war https://www.gog.com/en/game/men_of_war_assault_squad_goty_edition Other Men of War games:
https://www.gog.com/en/game/men_of_war_red_tide https://www.gog.com/en/game/men_of_war_vietnam Also, Condemned Heroes is good but is not available on GOG. A DRM Free version is available on Zoom Platform.
Close Combat series is probably among the easier recommendations. It is somewhat simulation like with the way soldiers will have their morale affected. I thought the way this was handled in Company of Heroes (a game where I am literally making equipment in the field and am basically training squads on the field) was tiresome. The highlight of this series is either Close Combat 2: A Bridge Too Far or Close Combat III: The Russian Front. I prefer either one for different reasons but would recommend one look up reviews on places like GameFAQs or a site that specializes in war games to decide between the two. That said, the depth here is also excellent. While the rate of fire of the M1 Rifle is still a little meh (bearing in mind that .30-06 is no walk in the park round) but the MG-42 is a beast as well as the flame tanks and flamethrowers on all sides. In these games those really valuable units also feel really vulnerable and you have to position them well and watch their backs in order to keep them going. Also, the units carry over in III I know and probably in II. It's kind of a question, if you ask me, between which setting you like more: Operation Market Garden or the Eastern Front. Worth pointing out, the Russian Front covers much more ground for a time period rather than the several days/weeks in A Bridge Too Far.
https://www.gog.com/en/game/close_combat_2_a_bridge_too_far https://www.gog.com/en/game/close_combat_3_the_russian_front You get the first game I think as an extra with either of those games, but I did not really like it. Any of the other games would also be fine. I should point out that after Battle of the Bulge the series is remakes until the Bloody First.
Now on to Sudden Strike. I really like the first game and the third game. The first game is the proto version basically of all the real time tactics games that followed, including the ones above. It feels like it but it is also a really fun game. It feels like a more grounded version of RTS games from the era. It has a lot of odd concepts if you are used to the game which came later, like using a sniper to kill tank crews to steal their tanks (I forgot which one this is from, between one or two but the point remains). This does not happen too much. The only real problem is that the maps almost feel too big for what it is asking you to do.
I love Sudden Strike 3 if only for the Iwo Jima map. It is awesome. This game has a lot of the drawbacks of the older games but feels nicely modernized as well. I did enjoy Sudden Strike 4 but did not like it as much as the other two games in this series. Since, I am to understand, some members of the old Codename Panzers team worked on this game it feels like a slightly uncomfortable mix of Codename Panzers and Sudden Strike. I would still get it.
https://www.gog.com/en/game/sudden_strike_gold https://www.gog.com/en/game/sudden_strike_3 There are tons of other excellent WWII games on GOG but the ones I linked to are what I would consider the best. If you forced me to pick a single game out of the above it would really hurt to say it's probably Assault Squad due to its versatility. It also has a good modding scene, but I would beg you to play any of these games vanilla thoroughly first.
I forgot about freaking Steel Division... just real quick, Steel Division II is largely Eastern Front oriented and reminds me of a much more in depth and detailed World in Conflict in gameplay. I have not played this game to my content just yet and would not feel comfortable endorsing it too much, but really it is an incredibly good game from what I have played.