The Knights-Errant are a diverse bunch, selected from promising and "inquisitive"individuals from across all the possible legions. More than this though, they are very loyal to the Emperor, the Throne World, and all that the Imperium stands for. They are the elites of the legions who are also the cast-offs, regardless of the loyalties of their primarchs or not (and Forge World, if you happen to read this, please let Omegon be Janus! Pretty Please?!).
Much like the legion praetor, these characters can be very customisable depending on what battlefield role that their controlling player desires to go in.
I think there are multiple (and good!) ways to build them. But all of them come with the standard Oaths of the Moment that should be thought about, the paragon bolter as well as the falsehood for pin-point accurate teleportation needs. The latter makes a number of possible Oaths of the Moment rather attractive. In particular, the Crusader objective is very easily attained by such a Knight-Errant. Others are tougher.
In their favour, that also sport 2+ armour coupled with an Iron Halo and a master crafted power weapon of their choice. Power Axes are probably going to be favoured here, but I can see cases for others potentially as well depending on the role that one sees for these characters.
The temptation with a customisable Knight-Errant character is to spend too many points making them in to some kind of uber unit. This needs to be avoided as an army is categorically not an army of one (despite novels of the same name!!!). The question is then: what battlefield role should your character have.
To try to answer the above answer, here is a few suggestions to consider and muse over.
Knight-Errant; Librarian, Level 2 Mastery (175 points).
This is a way to work in a psyker in to your army. Presumably, it will already have a couple of them in it already though? Frankly, at this points level, I'd be thinking of Tylos Rubio instead who is tremendous value by comparison! (maybe this will be FAQ'ed?).
Knight-Errant; Jump Pack, Power Fist, Melta Bombs (145 points).
Teleport in. Move around fast with the jump pack. Hit people in challenges with a power fist. Simple, but effective. Note the points cost -- its very reasonable for its purpose as well and can accommodate multiple Oaths. Take a Narthecium to taste.
Knight-Errant; Servo Arm (135 points).
Cheap enough to be a viable way to have a "repair" character in an army that needs to keep plenty of tanks at their peak performance.
Knight-Errant; Nuncio-Vox, Sniper Rifle (125 points).
With precision shot, hopefully this Knight can take out key figures in an open (i.e. not inside a tank) blob of troops?
Knight-Errant; Narthecium, melta bombs, lightning claw, combi-melta (140 points).
Place in a land raider with others and get the charge in? Not much point in the falsehood here though.
Knight-Errant; Narthecium, jump pack, melta bombs, power fist, combi-melta, plasma pistol, Librarian, Level 2 Mastery (215 points).
A near-ultimate build that can take on almost any role. Don't take it though: use something more specialised instead as this one is too general -- its a little bit too much of everything!