Arty is the most important: heavy arty will inflict loses, but remember that the most usefull effect of arty is to destroy ennemi morale: for that purpose, it is better to got 12 80mm mortars than a single 155mm gun.
When assault occurs in a really closed map BTW town,jungle or forest, use of arty will avoid you the 1-hexe ripost fire, that can destroy a half group,
because ennemy troops, when pinned, (taking cover), retreating or derouted will not detect you or fire at you.
Note that scoots and snipers are really hard to detect and could do a great job on already pinned groups....
For a good trainig at that sort of assault, play the given US Marines campain, which I find really interresting...