don't bother with WoR with bows, get outriders. in the new rules they have +1 courage, a courage special rule which allows them to use a heros standfast anywhere and they have a better shoot, for the same price
. i tend not to include to many archers on foot, might aswell just get a rider for the price of two and he can fullfill more roles, unless you want to volley fire, but you do not have enough men for that anyway. eowyn is a little weak as you said without any armour or a horse, you might find people pick her off for easy points, a normal captain or grimbold is best ( although its really up to you, they have better stats, she allows for more troops). cavalry and throwing spears work well, in priority ride to 7" away from your opponent ( make sure to show them and agree, you don't want any funny business with measuring). if you can fire and move back in this turn. then they either move to within an inch and face either losing priority and being charged or having turn one repeated, if they win, don't hesitate in using heroic move, they are very usefull, despite what some people say, to rohan it is your best friend (after the horses themselves), or they stay where they are, in which case move an inch, fire move back an inch, or they retreat, follow them, you have more move and if they give groung then it gives you more time to organise a charge with other units or will trap them.
here is my 600 point army:
eomer with horse, shield and throwing spears
8 rohan royal guard with 8 horses and 7 throwing spears and a banner
erkanbrand with horse
8 westfold redshields
12 helmingas with shields
600 points, 7 might (i think), 8 bows, 18 mounted models, 13 foot =31 altogether
the army should put grimbold in the middle, eomers unit should cover hug up a flank, harrass with the throwing spears and charge in with grimbold, erkanbrand should fire into vunerable units, go for archers (it may cost you a few riders) and then mop up any stragglers with another charge into the main fight.
this army has not had many battles and i tend to lose (mostly because the plan is there, but then i screw it up by changing it, which is stupid seeing as i spend so much time coming up with the tactics against opponunts, i then throw them out of the window and usually just mass charge
) someone else will probably ave better suggestions, but i would always take the named for rohan with the upgrades, they are just to valuable for a force which can just buckle against high fight or high armour.
hope this helped.