I've just discovered the joys of lancing, myself, so I'm riding across the map intentionally running into people for points. I took it up because I needed a counter to the dreaded spear ... besides getting off the horse. My polearm skill is so low I get 2-3 points every time I hammer some loser. I'm pretty sure it's riding skill that matters more.
The lance is quite possibly the cheapest of the most-effective weapons, unless you count the cost of the horse. I can finally see the usefulness of the Charger ... it was really tough hitting footmen from so high up with swords and the like, but with a lance you'd be in good shape.
Bastard sword ... a fine weapon, I truly love it. Dekes can't keep up with it 2-handed on the ground, and you can use it as a spear on foot against horsemen.
The morningstar is a serious can-opener, though. Its long spikes do "pierce" damage: that halves the effectiveness of armor. The bastard sword has a pierce attack as well, but you have to fiddle the mouse around to select it and it's really tough to aim. The stab is invaluable against mounted opponents and the major reason to choose a sword over a sabre, but it's a specialty attack, not something you can use all the time. The 'star pierces anything it hits, every time.
I would call the 'star a rider's weapon because it's so darn slow. On the ground you get creamed. The 2-H configuration bastard sword, on the other hand, is lightning fast. On the ground I'd rather have a bastard sword than a 'star.
I got a watered-steel sabre and thought I'd be invincible, but it can't crack armor. A bastard sword is just heavy enough to have some stopping power after a Deke's black armor absorbs the blow. Also, although for its speed the sabre has excellent reach, it doesn't come near that of the bastard sword, which is why with practice you can slice a Steppe Bandit off his horse without getting hit.
The sabre is also quite possibly the best bandit-killing weapon in the game, mounted or on foot. Speed and reach are a lethal combination against unarmored opponents. Just because I don't like sabers doesn't mean they're not great weapons.
In the early game the spiked mace is a poor man's can opener. It does armor-defeating bash damage and has adequate reach and speed for ground or horseback, and bandits and raiders routinely carry them. For the "nobleman capture" mission I use a balanced spiked mace rather than a slower, more powerful maul or warhammer.
Axes are slow and do slash damage, so I don't use them. I've never fought an opponent long enough for his shield to break, and the best way to neutralize a shield is a horse nudge, so I don't see much use for axes. It sucks getting your shield broken by them, however. That's why I sacrifice the coverage of a fat shield like a heater in favor of the virtually indestructible steel shield.
I hope these comments have been useful to you. Your best bet is to try different things and figure out what suits your style. A little side-note here: the polearms are almost always footmen's weapons. The glaive might look good on paper, but you can't slash with it from horseback, so on a horse it's basically a fancy spear.
