A marriage-based visa or green card is available to any foreign-born national whose marriage to a U.S. citizen is real and legally valid, and who is not inadmissible for any other reason. Procedurally and theoretically speaking, however, you have more than one option if you are coming from another country (and not already living in the U.S. and eligible to adjust status), as follows:
Whether you apply for an immigrant visa or a K-3, your initial application to come from overseas will be reviewed by a USCIS office in the United States. It will then be transferred to a U.S. consulate in your home country. The final decision on allowing you U.S. entry will be made by the consulate, after interviewing you personally.
For immigrant visas, it usually takes ten to 12 months from the initial filing with USCIS until the consulate’s final decision. However, your application could go faster or slower, depending on a variety of factors including the complexities of your case and the efficiency and workload of the U.S. citizen spouse’s nearest USCIS Service Center and the U.S. consulate in the immigrant's home country.
For K-3 visas, the time period between the initial filing with USCIS and the consulate’s decision to give the immigrant a visa to the United States is supposed to go faster -- but typically doesn’t. That frankly makes the K-3 visa an irrelevant option at this time (2016).
As always, however, times may vary, depending mostly on the workloads of the offices handling your file. Talk to an immigration lawyer for the latest on what's working and what isn't. Remember also that with a K-3 visa you’ll likely spend four to six months dealing with the U.S. government after you arrive in the United States and apply for your green card.
If you are interested in applying for a K-3 visa regardless of the fact that it may not save you much time, there is one important limitation to consider. You may apply for your visa only at a consulate in the same country where you held your wedding. Or, if you got married in the United States, you may apply for your K-3 at a consulate in the country where you (the immigrating spouse) now live). That means that, for example, if you held your wedding in Italy, but now live in Thailand, using a K-3 visa could be rather inconvenient, since you would have to travel to Italy for the visa interview.
The regular immigrant visa is much cheaper than a K-3, because you have to file far fewer applications with the U.S. government. This reason alone is why few people use the K-3 anymore.