In my opinion, for a really flexible build, you need Skill Points over Attribute Points. That's why I suggest going 18/15 build (Str/Agi). If you exchange 2 Attribute Points in for 4 Skills Points, you can come up with this build. I'm not sure how good it will be (haven't personally used it). But it's layout should fit your agenda. I'll discuss more below. Here's the build:
Level 30 (4 420 577 xp)
Strength: 18
Agility: 15
Hit points: 65
Attributes to skills: 2
Ironflesh: 6
Power Strike: 6
Shield: 3
Athletics: 5
Riding: 5
Horse Archery: 0
Power Draw: 0
Power Throw: 5
Weapon Master: 5
One Handed: 1
Two Handed: 1
Polearm: 120
Archery: 1
Crossbow: 1
Throwing: 106
Even though you'll go with 3 less Attribute Points, you'll actually be a stronger build. With 18/18, you would have to scatter out your Skill Points so much, or just ignore some skills all-together (like you had to do with Athletics).
With the build above, you have 5 Athletics and 65 hp... improving on the 2 issues you saw in your build.
Riding, Power Throw, & Shield: I gave you only 5 Riding, cause you still have 7 horses to pick from with it. Now unless you are just really wanting to use the Desert Horse or Courser (and they are a lot cheaper, both their cost & upkeep)... in which case, look at the build below. And if you plan on using melee from horseback (which I'm sure you are), then I'd definitely go with the more armored & higher-HP horses (for which you only need 5 Riding).
And I gave you 5 Power Throw so you can use Jarids. Now if you are like me, you love Heavy Throwing Axes and hate Jarids. If that's the case, I'd only go 4 PT, and put another point to Shield (for a total of 4 Shield, allowing you to use the Heavy Board Shield). Or if you really want to look like a Greek Hoplite, take points away from Athletics and go 5 Shield (allowing you to use the Huscarl's Round Shield).
WPF: I gave you 120/106 WPF (Polearm/Throwing). This can be altered. Personally, I'd go 130/90. Or you could meet in the middle at 125/99. A 90 in Power Throw should still be plenty of WPF even if you are wearing Heavy Armor. To be honest, I've not worn much Heavy Armor, so I lack experience. So you may want to 120/106 just to be safe. Though I honestly think 90 is enough, even for Heavy Armor.
If you really want 6 Riding, you can also go with the 15/18 Build (Str/Agi). If money is a problem, and you plan on going Cavalry a lot, you may want to look into the cheaper Desert Horse or Courser. Not to mention that the Courser is the fastest horse out there... while the Desert Horse is very maneuverable, and even cheaper. Don't go just 3 Riding to get the Rouncey. For it's price (and only costing 3 Skill points) it looks like a great buy. But trying to do melee combat on it, I got owned. Mind you I'm inexperienced at Cavalry... but with the Courser & Desert Horse having low HP as well, I'd think they'd be easy kills. Hence the suggestion to only go 5 Riding and use the more battle-hardy horses.
And with a 15/18 Build, you are sacrificing both damage and HP. However, you may gain a little speed in Polearms, with the extra WPF. Just want to give you the full picture. I personally suggest the build above... but nonetheless here's a 15/18 Build... with 6 Riding. And just as above, some things can be adjusted (like the WPF).
Level 30 (4 420 577 xp)
Strength: 15
Agility: 18
Hit points: 60
Attributes to skills: 2
Ironflesh: 5
Power Strike: 5
Shield: 3
Athletics: 5
Riding: 6
Horse Archery: 0
Power Draw: 0
Power Throw: 5
Weapon Master: 6
One Handed: 1
Two Handed: 1
Polearm: 130
Archery: 1
Crossbow: 1
Throwing: 108
I know it's a lot of info. But I like being thorough. I hope it helps. And personally, I kind of really like the first build (the 18/15 Build). It looks good... as far as numbers go. But will it actually be good on the battlefield... well that's a different story.
Maybe you can let us know?!