Alright, here's a pick/ban method that I've been using as my go-to kingdom card selection method. I'll give the 4-player version, but you can modify it however. I'm not sure if anyone else has suggested similar already.
Shuffle whichever randomizers you may want in the kingdom. Each player gets six randomizers (which only that player sees), and then two are played face up from the deck; these are in the "tentative kingdom". Each player takes turns. Each player has up to four picks and up to four bans.
To pick a card, less than ten cards must be in the tentative kingdom, it must be your turn, and you must play your randomizer of choice face-up.
To use one of your two bans, play one of your randomizers face-down on top of the card you want removed from the tentative kingdom. Put the two cards in front of you as a visual reminder that you used a ban. No one needs to see which randomizer you used to do this.
If you have picks remaining and there are less than ten randomizers in the tentative kingdom, then you must use a pick or a ban during your turn.
If there are ten cards in the tentative kingdom on your turn, you may use an unused ban, or you may pass. But you may not add an eleventh card to the kingdom.
Whenever a tenth card is added to the tentative kingdom, each player gets a chance to ban (if any remain), including the player who picked the tenth card. If no bans go out, then the tentative kingdom becomes the kingdom for the game, which is played as usual.
This method tends to lead to player X's least-favorite card never making it into the game. However, it also tends to lead to semi-random games where stupidly redundant cards do not make it into the kingdom. Playing with this method all the time will tend to cause half the cards to almost never get played, but it generally leads to fairly satisfactory games for all involved.
(picks per player - bans per player) * number of players + number of initial tentative kingdom cards = 10, and two bans is probably a good number generally, unless you want to go crazy.