Maybe a dumb question but when moving and executing close combat, how many action points do I check for spent? Is it cost of move plus cost of attack? I assume so since the unit is doing both in same turn.
Units don't move and attack on the same turn, even when entering "close combat". Close combat means that your unit(s) are in the same hex as your opponent's unit(s), nothing more. It does not mean any kind of free or simultaneous attack (which is unlike many wargames, and tends to trip some people up.)