You should file a fiancé visa petition on behalf of your partner. If approved, your fiancé would be issued a visa that allows him to enter the United States with the intent to marry and seek permanent residence. You must marry within 90 days of his entry. After you are married, your spouse would petition for a green card.
If you are a U. S. citizen, you can file the FORM I – 129F with USCIS to request the K-1 visa for your partner in Costa Rica. Once the K-1 visa is issued, your partner can enter the United States and both of you must marry within 90 days. After your marriage, your partner can then file the FORM I-485 with USCIS.
If you are ready to get married, you can file a fiancée visa. If your would like the person to visit the United States to see what it is like, you can seek a tourist visa. I think it would be a good idea to see an immigration attorney to discuss your options.