The Book of Knights and Ladies seems to be set up so that many players will end up playing bachelor knights, or other non-landed individuals. Is this correct?

"Pendragon is a game in which you follow the same family down through the generations and see their tale unfold in an epic fashion. Here, play this guy who won't have any inheritance or kids."

I'm happy to ignore this, but it seems that there could be interesting stories told here. Players would probably want to have a realistic chance of gaining land, a family, etc., though. How would you go about this?

Well, in the core book, it says you can choose to just start as the firstborn if you'd like. I always took those rules to only apply if you wanted them to. Plus, you get some interesting outliers sometimes due to the randomness of the system; I forget exactly how it worked, but one of my players rolled that he was the 7th-born son, but also rolled that he had only 2 sisters as his siblings, and none of the young knights in his family were brothers (a brother in law and a cousin, I think). We interpreted that as he being the only SURVIVING son, so therefore got to inherit the manner. Plus, you can try and marry well, or just do something to earn a holding of your own. While bachelor knights have the REPUTATION of not earning enough to support a family, plenty of them still did. I forget, there might be a penalty on the marriage table or something if you're not a vassal.

PK bachelor knights are allowed to marry, exactly for the reason of actually having a family. See Book of the Entourage 1.3 for more.

Also, note this in BoK&L: "Players may choose to make their first character to be the eldest son." The whole rolling for the son number is optional, and if you follow the default campaign assumptions in KAP 5.1 (character generation, family history), the first character is the eldest one, and likely the following characters, too.

It is actually not that bad playing a household knight, either, as long as the GM allows them to get married and have children. Some players are not that keen into the whole 'base-building' of the manor, and being at the Count's service 24/7 means that it is very easy for the GM/Count to send the PKs to do stuff. In a household knight campaign, a possible goal is to get eventually rewarded with a manor, perhaps 20 years down the line. In default GPC, a good opportunity comes in the aftermath of St. Albans in 495, when the kingdom is at Anarchy. Experienced, glorious, loyal household knights can probably expect to get rewarded for helping the Countess, or the more unscrupulous ones may try to seize some manors by force and try to get official recognition of their new status in exchange for swearing homage.

It is also possible, like Deacon Blues said, that the elder brothers might end up dead. Especially if they are PKs in our campaign. :P Or they might already be dead at the campaign start. For instance, if you look at the family history in KAP 5.1, there are plenty of opportunities to kill off the eldest brother in 479, 480 and 484, and simply say that his marriage (if he was married) was childless and hence the younger brother (the PK) inherits. Especially if the father was still alive, too, so that the eldest brother was never a vassal knight himself.

I would tend to expect (though I don't know if such an expectation is historically accurate - beyond William Marshal, anyway) that bachelor knights would be among the most likely to get to marry an heiress who is a ward of their liege lord. They will be the people whom the Count is most intimately associated with and probably trusts the most. They will have the most opportunity to serve him and impress him. They're in position to be the most grateful if landed. They have the smallest power base to add to whatever they gain through marriage.

I would think that the reason most household knights don't marry is because the Count doesn't want to pay for their family. Marrying them to an heiress is okay because she'll make them self-supporting.

I would tend to expect (though I don't know if such an expectation is historically accurate - beyond William Marshal, anyway) that bachelor knights would be among the most likely to get to marry an heiress who is a ward of their liege lord.

Yes, and the table in Book of the Entourage is intended to reflect that, in a way. A household knight with a long service is much likelier to have high Loyalty (Homage) and to have racked up a lot of brownie points with a liege than a vassal knight, so they'd have a better chance for an heiress, even though the actual number that needs to be rolled is the same as with a vassal knight. Also, they are likely to have more Glory than a young vassal knight.