I find it varies from faction to faction - playing as HRE it can take a while before any decent generals turn up, and you usually rely on those heroes (Albrecht der Baer being a major asset ). If I find someone who shows promise in the early game, then he'll get a lot of the jobs going to boost his stats and earn some V&Vs. Generally by the late era (assuming a start in early) then I typically have three or four 8 or 9* generals, and a dozen or so who are 5-7*, the rest being reasonably competent "also-rans". One of the best generals I had in one HRE campaign was a mounted X-bow, who ended up at 8*, valour 9 + VnVs, max weapon upgrade, and could trash kataphracts in melee.

I often find myself wishing the old king would hurry up and die so a bunch of "uncles" can be converted to governors to take advantage of their high command/acumen/etc etc. If in the process they get good provinces that add to their star-rating, then so much the better

When it comes to taking out enemy generals, I favour arbalesters. I usually keep my arb line with fire-at-will turned off, wait til the enemy are close, then toggle fire at will back on. That way you get an instant, mass salvo, which rips through the enemy charge and often as not causes most units to rout. Add to this one "sniper" unit targetting the general, and you can take out a RK unit quite quickly. Another favourite for this style of tactic are bashkorts, holding formation & position, with fire-at-will off until the right moment. A line of bashkorts like this can totally eliminate a unit of chivalric knights before their charge hits home. If any do survive the mssiles then they land straight on the spear points in such diminished numbers it's another insta-rout. These tactics are particularly suited for those Jedi-generals with the kamikaze tendency