My recommendation also.
You also get branching campaigns depending on your decisions, customizable vehicles (type of engine, type of armor, type of weapon or function and type of traction) and you can set the speed up or down in game with the slide of a bar.
The only points against it is that you don't really create units and each has a name, so fighting without losing them (though it's your choice if you continue when you do) makes it difficult later on, not only because you may feel attached to some, but each unit gains experience from mission to mission and losing a vet on a specific profession is enough for me to reload a game most of the time. Later stages get to be difficult if you don't figure out the best approach possible. I know I reloaded the final american campaign mission multiple times before realizing what the best strategy to beat it was.
I liked this game a lot, though. It's old 2D graphics (very crisp and clean) and it's not your typical RTS neither in gameplay nor in story. You can save anywhere, anytime so when the wife comes a calling you can give her the old "coming, dear" while saving your game and returning to your life. Once you beat it, you can always play it gain making different choices and seeing where they lead you.

On GOG:
Sacrifice - pretty simple and unique. Definitely worth looking into. It doesn't really meet your criteria, but it's something different and worth the investment.
The Earth games aren't incredibly simple, but you do get the pause, and the opportunity to research and assemble various unit components and weapons into super tanks.
Not on GOG:
Company of Heroes is one you should definitely consider. There is a pretty good demo that gives you a decent taster. It's essentially an evolution of Dawn of War's gameplay.
Darwinia & Multiwinia are both excellent. Pretty damn close to what you're looking for too.
Total War series - the most complex parts of the game are turn based, and therefore pretty much paused, the real time battles are awesome and definitely worth your time. But you won't be able to save during those so make sure you've got enough time before entering into those. I'd recommend Medieval 2, if only because the campaign doesn't disintegrate the way that Rome's does after a while.

Hostile Waters! Yes, I second that. I'd second Original War if I had played it yet. (too many games, too little time)
Darwinia is pretty cool indeed. I imagine Multiwinia is too.

These two things go together. Playing against the computer in TA, you can go defensive, but good players online will never let you do that. In fact they'll generally try to make sure you don't have the luxury of building as you please. And if you or the other guys manage to get a Big Bertha up, you/them pretty much deserve the arse pounding you'll get for letting that happen. Sounds like you definitely like a less challenging game.
Problem is, it's hard to find one that doesn't also have pretty poor AI.
Since you like simplicity and not micromanaging individual unit and group capabilities (I'm totally with you on that; didn't like that aspect of Dawn of War or Starcraft 3), I'd suggest Company of Heroes. It's a very fun and challenging game, and while no AI is good enough to come close to being as hard as fighting real live players online, it's still pretty decent. It's made by the same people who made Dawn of War and works pretty much the same, which you have noted you like.
Also FYI, I know Dawn of War had a more aggressive custom AI (many different AI's but one was kinda standard for people to use), and I think Company of Heroes might have had one too. Search those custom AI's out, because while some of them will just be weird or made by whiney people to make a game against the AI even easier, some are well balanced and can make the game much less predictable or tougher or more fun.

Oof! Thanks for all the recommendations so far: I think I'm going to try Original War (which I hadn't even HEARD of before this thread), and then move on to Sacrifice or JA. Company of Heroes looks awesome too, but GOG (for politeness, since is their forum, and for budget reasons, as I'm broke [see "married" above, ha ha]) games are pretty much my focus for now.

A new GOG game. Ground Control 2. It's good, but a bit short
Plays like World in Conflict (although the sides aren't generic and both the same)

Great description, Shepherd. I, too, like to be able to pause and then issue commands. I agree with you on the importance of simplicity. I stopped playing computer games for several years in part because it started to feel like I had to do hours of homework reading manuals and learning interfaces before I was going to get anything approximating fun out of a game. Simplicity doesn't mean shallow; just look at chess. I'll be following this thread with interest.
I know Fallout Tactics isn't exactly an RTS but I'd recommend it as it fulfills a lot of what you're looking for. It's turn-based squad combat -- no resource gathering to speak of, but it's fairly simple while retaining a decent amount of replay value, as you can complete missions in a variety of ways.

Company of Heroes would be a great tactical RTS, though a bit complicated, while anything Red Alert or Command and Conquer is good for just random fun.

Ah, don't forget Big Huge Games' venerable Rise of Nations. Great single player campaign, and a huge online following, both in coop and in player vs player. You can pretty much save anywhere, too, so that will obviate any time constraints you have to consider. It's complicated enough, but not quite as complicated as the Age of Empire series or not quite as in depth as the Civilization series. Still, maddeningly addictive!

Does anyone here play Soldiers: Heroes of WW2 besides ME!? It is a fun game if you WANT a challenge.

Hmmm... I've been thinking about getting it, only thing that's been preventing me so far is lack of funds. How good is it exactly?

Picture this:
You are in control of 4 Russian soldiers. Their goal is to board a train with one of their informants. Catch is, the enemy numbers are around 30+ and have 3 mounted guns and a tank. Have fun.
You get to manage their equipment, control them, it is pretty damn fun.

Gah why hasn't anyone mentioned this stuff yet???
Get Command and Conquer: The First Decade or download C&C 1 and Red Alert 1 online for free (youll need an older PC unless you get first decade)
Then get Age of Empires 2 gold, OR Age of Mythology gold
THEN get Rome:Total War. After beating that get Medieval 2 total war
and try command and conquer 3, you may like or hate it
if its simple fun you want age of empires 2 and command and conquer (I prefer the first one) are perfect for you.
And pausing during gameplay to issue commands is a total war feature.

By the way, wonder how did the original poster do with Original War? Love it, hate it, played a couple of mission and got bored?