Perhaps some chess techniques would be a good start.
You mention assigning each move a score, but I don't think that would provide a convincing opponent. What I would suggest, is making a system that gives the current state a score, like - give each unit type a value, like 2 for a soldier, 5 for a tank, 10 for a bomber plane etc etc. Now, for each unit, you'd check if it's under threat, then decrease it's value, if it's threatening an enemy unit, then increase it's value. So, at any point - you'd have a score for each player, which basically determines who is winning, but in chess AI this is very important.
If you can determine a score for each player, for the current state of play, then you can simply test each possible move and keep a record of that move, and the score. Maybe you'd need a macro language to do it neatly, like to hold the info for the move. Anyway, say you make a list of every possible move, calculate each moves resulting score, then repeat that, adding the most obvious opponent move, then repeat, repeat, repeat. Your still selecting a move from that original list - but all the time you'd look for the best possible move - the move that results in the best score in the long run. If you have a powerful unit, maybe it's value is 10 times what other units have, well the AI would automatically try and get rid of that unit, because it would have the biggest impact on the players score. If 4 moves ahead, the AI can possibly get rid of that unit, then it will. It'll also defend and attack sensibly... looking for the best defensive positions, pieces would move out of harms way if they can, units would even sacrifice themselves if it benefits the cause.
This is a very mechanical and precise way to calculate AI, you might actually have to add in some randomness (even add a random value to the move score to mix it up a bit).
I guess my point is that AI isn't too scary when you consider that it could just be a sum, based on the units in play and how much of a threat they are, or are under. A game like Civ at least allows a grid style and turn based movement, really I think the old chess brute force approach would work pretty well and you'd get results fairly quickly, maybe start with just calculating the first move - that would at least get the enemy AI going, and make the project much more interesting to work on.
I am the one who knocks...