Welcome to Talkbass!
White Wedding sounds like you need to cut some of the tone on the bass and play with a pick (if you're not already, as being used to playing guitar I'd assume you're already using a pick, but you might want to move up to a thicker pick like 2-3mm).
As far as effects go, I'd highly suggest going over to the effects forum. There's literally tons of information about what effects (if any) were used on bass in specific songs. (for example: the dying battery in a Mutron III envelope filter sound on the bass in Sir Psycho Sexy by Red Hot Chili Peppers that can be done with an Electro-Harmonix Bassballs) You can also find information about pedals that sound like certain types of amplifiers or overdrive/distortion that certain old tube amps generated in recordings. (for example: the Tech 21 VT Bass or Catalinbread SFT. Both of which are modeled after Ampeg amplifiers and are very versatile pedals.)
My only warning is, the more you read things on this forum, the more things that you want to purchase.
You will soon become intimately aware of the acronym: GAS (Gear Acquisition Syndrome)
Wallet beware! Your best bet is to find a way to be happy with what you have for now before it makes you poor. If you don't believe me, check my profile and you'll see how many different effects I've played around with.
