Be aware it might be difficult to get both a 1:1 figure ratio with 15mm figures and company- to battalion-level decision-making in a playable game, due to the physical constraints of space and time. A WWII battalion, even with a company off-table in reserve, probably means 200+ figures on the table.
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For the command level you're looking for, Crossfire by Arty Conliffe is fantastic! Its activation system heavily emphasizes terrain and tactical decisions around its use. A company-size game lasts about an hour, a battalion game about 4, including teaching new players.
A typical player force would be one Company HQ, 3 Platoon HQs, 9 rifle squads, possibly a light mortar stand aggregating the platoon mortars, and a couple of attached support assets like MMG squads, Forward Observers for off-table mortars, or the occasional infantry gun or AFV.
Each of these units is a single stand, so you're looking at ~15 "pieces" in 3-5 groups, since each platoon stays mostly together. The combat mechanics have no technical minutiae, with the only distinctions being training, SMGs, MMGs, AT weapons, engineer equipment, and AFV gun/armor stats.
It is not a "tournament-style" game, the activation mechanics not being well-suited to the sort of symmetric meeting engagements you usually see in other systems. It is prime for attack-defense scenarios, though.
I play it in 6mm at a 1:1 figure ratio, and a company-level actions fits on a 3'x3' card table, with a battalion-level game closer to 6'x4'. Playing it with 15mm figures might mean accepting a 1:2 ratio for infantry to fit in a reasonable area.
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If your priority is individually-based miniatures, I'd recommend Chain of Command by Too Fat Lardies. It's a platoon-level game emphasizing the positioning and actions of leaders at that level. It plays in 1-2 hours, with the rules for company-size engagements going 3-4.
A platoon in CoC would be 1-2 senior leaders; 3-4 squads each consisting of a junior leader, a 3 figure gun team, and a 4-9 figure rifle team; and 0-6 support elements consisting of additional squads, support weapons, observers, guns, or AFVs.
Each miniature is tracked individually (although you can multi-base them and most people do so for support weapons), so that's 30-60 "pieces" in 3-15 groups. Most weapons are just a range and a firepower stat, and most weapons in a given category have the same stats, so again it's fairly accessible, although there are some more complex charts for close-combat and morale.
As far as gameplay, Chain of Command is equally well-suited to either pick-up games (with a clever pre-battle phase), scenarios, or full-on campaigns.
I play in 15mm, and a platoon-sized game has lots of room on a 6'x4' with realistic-ish spacing between figures and units. Two platoons apiece (or playing in 28mm) starts to get a little cozy, anything larger definitely needs more space.
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Also, the 5Core system is worth a look. It handles each level of combat with a module based on the same core mechanics. Very accessible, albeit somewhat generic.
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In short, there are some great options out there, so consider which factors you listed are most important. Good luck in your search!
opens the box on a Battlefield in a Box house.