"Company of Heroes" (formerly known as "New Steam version") is the version that is supported by Steam. It has working multiplayer, Steam-workshop integration and needs to be installed in order for mods on Steam to work. INSTALL ONLY THIS VERSION, NOTHING ELSE!
"Company of Heroes - Legacy Edition" is the "old" version from before Steam took care of the game. It isn't supported, doesn't receive updates and doesn't have a working multiplayer.

"Company of Heroes", always, nothing else. There have been reports in the past that installing anything beside it will cause problems with the game and most "Campaign/faction XY is locked" issues can be solved by uninstalling everything but the base game. Same goes for "Can't connect to Relic Online" issues because Relic Online isn't in use since 2013 anymore.

On the Legacy Edition store page, the following disclaimer can be found:

"Company of Heroes" is the newest version, updated and maintained by Steam. It contains all the files, including the DLCs, so no additonal downloads are needed. However, the DLC files are locked until you purchase them, which unlocks them automatically. If you just want to play the game, "Company of Heroes" is all you need.

You will ALWAYS receive "Company of Heroes", even if you, for whatever reason, don't purchase the base game but only a DLC. In this case, running "Company of Heroes" will grant you access to all the DLC files, but everything else will remain locked.

"Company of Heroes - Legcay Edition", "Company of Heroes: Opposing Fronts" and "Company of Heroes: Tales of Valor" are outdated and obsolete. Installing them might cause problems with "Company of Heroes". Only do so if you know what you are doing (which means you probably don't need this guide in the first place).

No, Steam only sells them together.

No, you pay for "Company of Heroes" and get the Legacy Edition for free (which, technically, still works). To quote an announcement from 2017:

We did not want to remove the Legacy Edition altogether because:

• some of you guys are still playing it, for various reasons (including old mods)
  
• COH1 total conversion pages are tied to it in the Steam back-end, and we can't change that
  
• most of the reviews for COH1 are tied to it in the Steam back-end, and we can't change that / transfer them to the newest app

Addionally, the Legacy Edition comes with the map editor.

Two DLCs, „Opposing Fronts“ and „Tales of Valor“.

OF: Two new factions (Brits and Panzerelite), two new campaigns (one British, one German)

ToV: Three mini campaigns with three missions each. Those missions take place on one map per campaign. Tiger Ace and Causeway are way more arcadey than the rest of the game (you play super strong units and have a new feature called "Direct Fire"), while Falaise Pocket feels more like the missions you already know.
For Multiplayer: Panzerkrieg is PvP, Assault is PvP with AI support, Stonewall is PvE.Once again, Panzerkrieg and Assault are arcadey, Stonewall is closer to the original gameplay.
You also get two new vehicles per faction to optionally replace other vehicles and a skin for the Tiger tank once you complete the Tiger Ace campaign.

https://test-steamproxy.haloskins.io/steamstore/app/9340/Company_of_Heroes_Opposing_Fronts/
https://test-steamproxy.haloskins.io/steamstore/app/20540/Company_of_Heroes_Tales_of_Valor/

You don‘t need the base game to play Opposing Fronts. You can still play with and against players who own it, but you don‘t have access to the base games campaign and factions.

Tales of Valor doesn't need the base game to run anymore. According to someone at the forum, it is possible to play with all factions in multiplayer just by owning Tales of Valor. According to someone in the comment section, you only get Brits and Panzerelite. I can't say what's true.

Depends on your personal preferences. Wait for a sale and get them there if you are unsure.

In my personal opinion? Yes. You should get Opposing Fronts merely for the fact that it adds two new factions and campaigns.

No, only install "Company of Heroes", it contains everything.
Both, „Company of Heroes: Oppsing Fronts“ and „Comapny of Heroes: Tales of Valor“ are leftovers from the time before Steam took over the game. You can download and run them, but both will be outdated and might have technical problems. Just like the Legacy Edition.

I'm not entirely sure on this topic, because the people reporting this issue are usually very unclear in doing so. My guess is that people confuse the text on the loading screen and main menu with the actual content loaded. So yes, even if the loading screen reads "Tales of Valor", you can still access all the content of the base game and Opposing Fronts (if you bought them, of course).

In case you can't, make sure you have uninstalled everything but "Company of Heroes".

Mods for Company of Heroes aren't listed in the workshop. Search for „Company of Heroes“ in the shop or use this comprehensive list.

My personal opinions:
Back to Basics: Anti-fun changes to the AI, I only finished one match, gave up the other two because of frustation, felt more like a battle of attrition than the usual dynamic CoH gameplay
Battle of Crete: Small scale combat, nothing to write home about.
Blitzkrieg: Review. People will pay you money to get their hands on .exe files of earlier versions.
Eastern Fronts: Probably the most popular mod. Having Soviets is nice, Ostheer not that much, worth playing if you don't like CoH 2
Europe at War: Review.
Europe in Ruins: Never played
Far East War: Can feel unbalanced, older tanks and more artillery.
Modern Combat: Cool ideas (Javelins, TOWs) that don't always work, some localization errors, can feel unbalanced in favor of the PLA
The Great War 1918: More focus on trenches and artillery (the AI can handle neither), just don't expect big battles like in the real WW1 because unit upkeep and production speed weren't adjusted.

Download from the Steam page, start the mod you want to play from your Steam library

The according community hubs. Just like Company of Heroes, every mod has its own forum on Steam. If you have problems, you should ask there.

Unlikely. I heart something about Steam not adding new mods, but I don't remember where. They added the Back to Basics mod in July 2021, so... maybe?

Depends on the mod. The team has to update it so that it works with the current Steam version. Some mods come with an installer-exe, some need you to change the launch options of the game. Make sure to check the ReadMe-files of the mod you want to play.

In case the mod wasn't updated to work with the current Steam version, it might be one of the very few cases where you have to install the Legacy Edition.

This guide is based on a (now locked) thread I made a while ago because many people asked the questions mentioned above. I decided to turn it into a guide because
a) I don't have to bump a guide
b) Guides have better formating options and are easier to update
c) I believe it's easier to find this way

If you still have questions or feedback, I post below.

Thank you.