If considering K-3 think carefully about it. CR-1 and K-3 tend to take about the same time, K-3 may save you about a month, however the K-3 has the added pain of adjustment of status, and it NOT a work authorized visa, so also has the added period of limbo waiting for EAD to be able to do things like take a job, get SSN, etc...
For the most part CR-1 tends to take a bit longer than K-3 to get if you prepare for NVC when they request I-864 fee, and Visa fee, as well as documents requested by NVC. In many cases the CR-1 petition reaches the consulate just before K-3 interview, which causes K-3 to get dropped and the interview becomes a CR-1 visa interview.
K-3: I-130: $355 I-129F: NONE Consulate: $131 AOS: $1010 ($1496)
CR-1 I-130: $355 NVC I-864: $70 NVC Visa fee: $400 ($355+$45) ($825)
I see many posts from K-3 holders stating, "Wow this sucks, I am stuck at home because I don't have EAD, DL, etc, or I am having hard time getting added to bank accounts because of NO SSN." K-3 has a 90 day or longer period of limbo while waiting for EAD or Green-card.
K-3 was developed at a time when CR-1 was taking much longer that today, NVC has greatly streamlined the CR-1 process to the point where K-3 becomes irrelevant.