Title kind of speaks for itself. I've found the hardest thing in battles is coordinating. I generally end up just choosing one or the other form of attack, because of the difficulties in having both. Long range, big gun weaponry can cause as much damage to your own units as enemy ones, if you have short range fighters in the middle of the fray. Is there any strategy to combining these two types of attacks in a battle?

In a word: no.

If you're using anything with an area effect (ie. artillery, cannons, air cruisers, bombers, grenaders, assault mechs) then keep your other units out of the way because they're going to get hit indiscriminately. However, all other units with ranged attacks (eg normal lasers) are safe to use with melee units and won't ever hit their own side afaik.

One exception is if you're being strike rushed you can use a combination of mounties and grenaders. If you get it right (and it's extremely tricky), you could use mounties to herd the strikes towards the grenaders (and it helps if there's a turret nearby as well). There's not so much risk of friendly fire here because grenaders do very little damage to non mech units. If you're lucky and if you can out-micro your opponent, you might be able to overwhelm the strikes.

Apart from that, I'd say the best way to combine the various forces is to use the long ranged area weapons to attack the enemy and keep shorter ranged and melee units back to defend them. For example, cannons and artillery are both very vulnerable to mounties if they get inside the minimum range, so it pays to have some troopers hanging around to protect them.