The dark-colored Poke Balls (Ultra Ball, Luxury Ball, Dusk Ball) and the sleekly-designed Poke Balls (Luxury Ball, Premier Ball, Cherish Ball, Anime!Sport Ball, GS Ball/Park Ball, Dive Ball, and the Master Ball with its lovely spray of stars) tend to be by favorite Poke Ball designs. Most of the game designs are pretty good, although the Dream Ball just looks BLEH. :x
As for catch-rates, the Repeat Ball is usually my go-to for Generation 3 if I need a scapegoat or utility Pokemon... The Quick Ball will likely be useful in post-Generation 3 games.. Other than that, each Poke Ball is designated to catch a certain sort of Pokemon, paying no mind to the capture rate or "intent" of the Poke Ball's use.
I do feel it's sad the Apricorn Poke Balls are confined to just being in the Johto games, it really sucks for those who wanted to see them in other games.
This issue is an intense aggravating flaw for me for all of the post-Generation 4 games so far, especially since Game Freak takes the time to have the Apricorn Poke Ball designs repeatedly sprited/modeled
and coded into each game that subsequently follows
Pokemon HeartGold/SoulSilver (to apparently maintain consistency for any Pokemon originating in
Pokemon HeartGold/SoulSilver). >:( Seriously, Game Freak, just do what you did with the Boon Island/Two Island Market Stall and have a random salesman import the things from Johto and sell them for a reasonable price! You don't see Devon Corporation of Hoenn hogging all of their Timer Balls and Repeat Balls; why must the Apricorn Poke Balls of Johto be any different in exclusivity/rarity?