Honestly speaking, "moving first" is not always a good thing. To give you an example: 1. Player unit(knight) moves forward 5 spaces. 2. Player unit shot by enemy archer. Archer then moves out of strike range of knight.

This is sort of how FireEmblem by Nintendo does its AI calculations. Their AI seems to be "always wait unless player unit is in striking distance." In the game, it is the player that gets first move, but usually the enemy that gets first attack.

What worries me about this approach is your small board. 64 squares with already 16 of them filled. . . Approach #1 might not work very well when both sides are so close together.

As for approach #2, this is similar to what Tactics Ogre by Quest did on the SNES. Each unit was given a Wait Timer, and when it became zero, they were allowed to move/attack. If the player played in a "normal" way, it usually became, "player moves 1, enemy moves 1, repeat" type situation. Of course, you could make it so that your party is comprised only of a certain type of unit. Then, usually they would all move together en masse, sort of like #1.

I tend to like option one, with a few adjustments. Instead of a speed based attack thing have every battle phase take place simultaenously. ie. when player A unit attacks player B unit, they both fight it out at the same time, perhaps with the attacking piece getting an initiative bonus or something of the sort.

Say A has an armoured vehicle with a weapon 5 and an armour 15
and B has a cannon with weapon 18 and armour 3

If A attacks first his 5 weapon will destroy B''s canon cuz the armour is only 3
If B attacks first then HE will destroy A becuase his 18 weapon will destroy A''s 15 armour.

Therefore the main advantage the attacker will have is that he gets to choose whether to be on the offensive or defensive.

Or perhaps the defending iece only fights at 75% it''s total capacity or something.

Although I also think 16 pieces on a 64 tile board is rather crowded.

If you want to check out a game that uses option #2, check out MageKnight. The rules are downloadable from their site.
www.wizkidsgames.com/mageknight