Astaroth is the go to for all Grabbing. His range damage and ability to throw grounded, crouching, standing, and jumping is unbeatable. However if you want to depend on throws Rock will use them more simply because everything wants to go into a grab. You could theoretically play Astaroth more throw oriented if you want but he has more options than rock so doesn't always need to, thus is the illusion Rock is more throw oriented. In reality Rock is just throw dependent, he has no viable options.
Ivy is a beast in throwing, but it's more of a scary tool than what she plays around. If you can do iCS/SS you can scare your opponent into other stuff rather than ever need to use it.
If none of these appeal to you, I suggest using characters with crouch throws or go the Seig/Nightmare route. Crouch throwers will constantly put you in jeapardy of throws and help beat 2G to avoid the scenario so you can have an aggressive game and go into any throw when they start to turtle. AS for Seig and Nightmare they just have RIDICULOUS range and can do the leg throws that can catch people off guard.
Algol has good throws, but his playstyle just doesn't let you utilize the option very often.
Honorable mention: Vader.