***Moved to "What visa Do I Need" as OP is asking about both options.***
Forget about a K-3 visa. They are obsolete, and are very, very rarely ever issued. There are significant differences between a K-1 fiance visa and a CR-1 spousal visa. My advice is to spend some actual time together before making a decision. Marrying on the first visit is NOT a good idea. Multiple visits is always a better choice. This is especially true when there are red flags such as a large age gap. Here is my analysis between a K-1 and a CR-1:
Every couple has their own priorities, and each couple must decide which visa is better for their situation.
K-1
More expensive than CR-1
Requires Adjustment of Status after marriage (expensive and requires a lot of paperwork)
Spouse can not leave the US until she/he receives approved Advance Parole (approx 6-8 months)
Spouse can not work until she/he receives EAD (approx 6-8 months)
Some people have had problems with driver licenses, Social Security cards, leases, bank account during this period
Spouse will not receive Green Card for many months after Adjustment of Status is filed.
A K-1 might be a better choice when 18-21 year old children are immigrating also
In some situations, marriage can affect certain Home country benefits, making a K-1 a better choice
A denied K-1 is sent back to USCIS to expire
K-1 entrant cannot file for citizenship until after having Green Card for 3 years.
Once an I-129F has been approved, delaying the case is difficult to impossible if the need arises.
CR-1/IR-1
Less expensive than K-1
No Adjustment of Status(I-485, I-131, I-765) required.
Spouse can immediately travel outside the US
Spouse is authorized to work immediately upon arrival.
Spouse receives Social Security Card and Green Card within 2 or 3 weeks after entering the US
Opening a bank account, getting a driver's license, etc. are very easily accomplished with GC, SS card, and passport.
Spouse has legal permanent Resident status IMMEDIATELY upon entry to US.
The clock for citizenship filing starts immediately upon entry to the US.
A CR-1/IR-1 case can be delayed indefinitely at NVC if the need arises.
What does that mean?