Good advice so far. I'm a 13th gen cavalry lancer (and a few gens on an alt I used for retiring for heirlooms), so I some advice of my own I"m always willing to share
When you retire, heirloom your horse first before any other heirlooms to +3 (and then your weapon 2nd). There's different tips on how to do this the best that I won't go too far into, but you have options like saving your first two heirloom points, and trying to sell those + some gold for a +3 item. Otherwise you could sell your first heirloom point and never have to worry about upkeep again (400k gold or so).
For builds I'd suggest going minimum amount of agility needed for riding the horse you want to ride. Typically for any cav class that is not using a shield, I would go 24/15, 21/18 or 18/21 (at level 30) depending on horse you want to ride. For classes that use a shield, then drop 3 strength (so 21/15, 18/18, or 15/21).
For lancer cav, I prefer my courser since I am riding fast. However a destrier is certainly acceptable as well (I'd probably stay away from armored horses since they are slower and you won't be getting that much needed speed bonus, since lances are pretty weak compared to a 2h or 1h weapon on horse). The arabian warhorse is my favorite horse in the game, but for me going only 15 strength is too low, so not worth the trade off.
I was always a 1h/polearm/shield cav. At level 30 I was always 18/18 (since I decided to ride a courser). In hindsight I wish I would have rode a destrier so I had more strength and power strike, but c'est la vie (sp?).
As a lancer, I prefer the heavy lance because I can go up against anyone else on horse and never have to worry about them having a reach advantage (including great lancers, you can outreach them if you time it right). However when the heavy lance was weaker than it is now, I was a regular lancer for many generations, and it is by far the best lance if you can refrain yourself from going up against people with heavy lances. It destroys infantry (that 10 less length isn't going to hurt you vs infantry if you are playing correctly) because of it's high damage output, and you can hit more infantry per minute than a heavy lance due to the increased speed.
However as someone starting out without any heirlooms, using a regular destrier and a heavy lance would not be a great choice. I only really like my heavy lance because it is +3 heirloomed, I have 24 strength, and I'm riding the fastest horse in the game (+3 courser). I would highly recommend having you use a lance on a destrier and using either 24/15 or 21/15 for your build. I really like having a shield, so naturally I also have some 1h WPF as well. Shields protect you very nicely from ranged, but also just as importantly, from someone who has you dead to rights with a couched lance you can't avoid (technically you can chamber block a couched lance, but that is not very easy from horseback and without practice).
Also if you choose to use a shield, use a 4 skill shield (either the elite cav shield, or my favorite, the knightly heater shield. There's also some other really good 4 skill shields out there like the knightly kite shield)
Now for build suggestions:
These are what I would suggest for you (you can play around with your builds using an updating character calculator that San created:
https://googledrive.com/host/0Bzs1vJv0tQLHZ3AwLUQ0Tkt0djg/calc.html )
24/15 Pure polearm cavalry riding destrier or barded warhorse:
Strength: 24
Agility: 15
Hit points: 59
Skills to attributes: 8
Power Strike: 8
Athletics: 5
Riding: 5
Weapon Master: 5
Polearm: 139
21/15 (1h/polearm/shield) this is the build I'd recommend using, also recommend a lance + destrier :
Strength: 21
Agility: 15
Hit points: 62
Unused attribute points: 1
Skills to attributes: 2
Ironflesh: 3
Power Strike: 7
Shield: 4
Athletics: 5
Riding: 5
Weapon Master: 5
One Handed: 108
Polearm: 108
21/18 lancer cav (on courser) this is a pretty weak build compared to the 21/15 or 24/15, also can play around with IF and WM distribution:
Strength: 21
Agility: 18
Hit points: 56
Skills to attributes: 8
Power Strike: 7
Athletics: 5
Riding: 6
Weapon Master: 5
Polearm: 142
18/18 This is the build I always went with at level 30, 1h/polearm/shield cavalry using courser:
Strength: 18
Agility: 18
Hit points: 55
Skills to attributes: 2
Ironflesh: 1
Power Strike: 6
Shield: 4
Athletics: 6
Riding: 6
Weapon Master: 6
One Handed: 125
Polearm: 124