As far as I can remember it doesn't matter which option you choose when launching the game - all content from installed (i.e. purchased) expansions is available regardless of which version you choose to launch. (Although I'm not sure if launching the original vs the "New Steam Version" makes a difference)
Company of Heroes (New Steam Version)
If you play multiplayer online then you will want to install this version instead of the original - Earlier this year the CoH team switched its online system to Steamworks after it found out that the existing online system being used was being terminated.
This update is totally free for owners of the game and is identical in all other respects - you shouldn't notice any differences between this and the standard "Company of Heroes" option, except for the fact that you can still play the multiplayer.
For more info see Servers for COH1 to continue on Steamworks
Company of Heroes: Opposing Fronts
Company of Heroes: Opposing Fronts is a stand alone expansion for the original Company of Heroes, which means that you don't need to own the original Company of Heroes in order to play the game, however it acts as an expansion of the original game if you do.
This expansion added:
- Two new factions, the British (as an Allied army) and the Panzer Elite (as a German army)
- Two new single-player campaigns played from the perspective of the German and British sides
Note that owners of Opposing Fronts and the original game are able to play against each other in multiplayer matches, however players are restricted in their choice of armies (e.g. a player that owns only Opposing Fronts is only allowed to choose from the British and Panzer Elite armies).
See Company of Heroes: Opposing Fronts for more information.
Company of Heroes: Tales of Valor
Company of Heroes: Tales of Valor is another stand alone expansion for the original Company of Heroes, which again means that you don't need to own the original Company of Heroes in order to play the game - if you do then the additional features of Tales of Valor simply appear as additional options in the original game.
This expansion added:
- Three new short single single-player "episodes" (short campaigns), focussed on using fewer more powerful "hero" units to complete missions
- Three new multiplayer "operations"
- Assault, a 3v3 team-game mode in which each player chooses a "hero" unit which fights and assists AI controlled troops around it in order to fight towards and capture the opposing players bunker
- Stonewall, a co-operative team game in which 4 players defend a small town against waves of attacks
- Panzerkrieg, a mode similar to *assault with hero units replaced by tanks
I'm not sure what other multiplayer options are available for players who only own Tales of Valor and don't own any of the other games.
You can find more information here Company of Heroes: Tales of Valor