My Peruvian Girlfriend

The U.S. citizen marries the foreign
fiance in the USA or in another country (could be home country), the foreign fiance goes back to his/her country, the U.S. citizen applies to the Service Center for an I-130 spousal visa petition.

This was the only option until the K-3 process was invented. The K-3 is most often faster to reunite families.

This is basically the 1st half of the K-3 process. If you file for a K-3 you are filing to get an IR-1 / CR-1 by default (filing an I-130) as well as for the K-3. The K-3 was designed to allow the foreign spouse to enter the US even if the I-130 has not been approved. In most cases this works out well since the I-130 takes so long to approve and the K-3 is relatively fast. In some cases the I-130 is approved fast enough though that this option is better then a K-3 (or if the applicant applied for a K-3 -- i.e. filed an I-129f -- then they can abandon the K-3 and pursue the IR-1 / CR-1 instead).
• can work upon entry (no restrictions)

• This is an "immigrant" Visa and will as such allow the applicant to arrive in the US as a permanent resident.

• They will not require an Advanced Parole document to leave the US for travel or require an EAD to work.

• As of April 2005 many applicants have reported that IR1/CR1's are faster than the K-3 option. This may change at any time though.
• Separation from family for sometimes longer then the K-3 or K-1 visa option. Applicant will most likely not be able to enter the US during this time.