Action Points Allowance...

You mentioned having Basic and Major characters. You could assign the different units a "Base" amount of action points, and then add the roll of a D6 to that base number. So the player knows that their major unit will ALWAYS be able to execute their base number of action points, and the extra points from the D6 allow them to carry out more, or more exciting actions. (Although, you might want to treat the D6 as a D3, to cut down on the number of action points being handed out.)

If you want the players to manage the action points I don't know if dice is the best way to go. Your introducing a lot of variability such that the decision-making of the turn goes from preplanning to reactionary (do the best with what you rolled). The previous posters ideas help. A fixed amount with the option to risk it for a higher amount or a fixed amount with a roll or a customized die with the low numbers balanced out with other functions.

The card idea I like except I would have the player manage it themselves instead of drawing it. Give each player a hand of AP cards. Each turn they choose one to play but can't use it again until their hand runs out. That way they have to make interesting decisions of when to use their high AP cards.

Just my 2 cents.

Dice are fun but not if they slow the game down to a crawl, they take time so unless each player only has a single unit or so, I would go for fixed points; also this makes a player better able to prepare her turn and set up strategies without waiting to see the die result.

I like an idea where you have a hand of cards each with an action point value, and each turn you draw a new card/s back up to a hand limit. To make it slightly more interesting though when you play your action point value card, the other player can then play AP cards until he passes your value.

Example:
Player 1 has 3 AP cards 1, 3, and 4. He decides that he needs to play the 4 AP card. And takes a number of actions = to the value of the card.

Player 2 has 3 AP cards 2, 3, 4: he decides to play the 2 and 4 to give him six action points and places him ahead on the AP value.

You could even go the path of Horus Heresy where action cards all have a AP value and you need to manage your hand. The upside to this is you can really differentiate different sides by the kinds of actions that can be completed.

Quick idea that could fit your need. Maybe not all units requires an action point to move.

In one of my game, when leader units moved they could bring adjacent units with them without having to spend extra action points.

I'm inclined to agree with the idea of consolidating the cards. Heck, you could use that as a balancer. You have a hand of cards, some will give you more AP, some will have other effects, like drawing more cards or buffing units and some will allow you to attack at various strengths or whatever.. Or combinations of these.. like a card that will give you 2 APs or draw 2 cards... or 3 ap or +1attack etc. This way it becomes less about I have action cards and attack cards and it becomes just cards.

The word is actually replenish (sorry for the typo, I was using my phone).

I'm actually a big fan of the face up draw options, like in TTR. I've used it in a number of prototypes myself. If I may suggest another method for balancing crappy card draws. Maybe the players can earn extra SP by discarding cards without effect.. So if you have three cards in your hand you don't think will be useful, you could discard them to get 3 SP instead of whatever was on the cards.