I've found that Rohan is a challenging and unforgiving army to play, but very rewarding when played correctly (maybe its because you know the odds seem stacked against you
).
First piece of advice i would offer is that the original Eomer profile, along with Erkenbrand are the two best heroes in points value terms, Theoden's points value is way off for the profile, which is unfortunate given the nice sculpts, whilst Grimbold and Eowyn are nice characters who can add some flexibility to an army.
I'd be wary of going with a full cavalry army as you pay for bows you cant use, and will find you need to use a lot of points on heroes in order to make sure you can keep heroic moving and avoid getting charged (and slaughtered in the process, its essential you have a hero with cavalry to allow you to dictate which fights they take part in even when priority swings against you, if you cant ensure charge bonuses your riders are no better than warriors with big bases that end up swamped
).
Another thing i've found is that royal guard can be indispensable, they're a great and reliable improvement over standard warriors, i tend to take a number on foot to mix in with basic warriors and like to give them throwing spears as i find they tend to stick around longer, im sure they work just as well mounted. Throwing spears in themselves are also great items of wargear but taking too many can really eat into the points you have available; they aren't cheap pieces of kit.
Upgrading some warriors to Helmingas is another good way to make an army more "killy" but they do require you to take grimbold, who, whilst as good as a captain, cant really lead an army alone, so you'd need at least a second hero with any cavalry, not sure how feasible this is at 500pts but its worth considering.
Finally, banners can be a good way of compensating for a lack of standard spear support, but again cost a lot of points.
All in all, Rohan offers quite a diverse range of tactical scope in combinations or foot and mounted troops, reasonably priced but effective heros and a few different types of infantry with interesting upgrade/wargear options, balancing a mix of these troop types has worked best for me in the past, but experimenting with a few different lists should give you an idea of how you like to play and which troops you like you use, hopefully my brief reviews of each type has helped shed some info on Rohan lists at any rate.