Here’s what I know (from personal experience):
What she needs to exit from cuba is (roughly in order)
1. An invitation to visit your country (ie a letter sent from you to her)
2. A passport - she can obtain this by simply purchasing one (about $200 I think)
3. A tourist (fiance) visa from your embassy
4. A “carta blanca” - i.e. permission to exit the country. This is the tricky bit. It doesn’t cost much, but can take a long time to get or may be refused for any number of reasons, e.g. if she is deemed to work in an important job. Any person involved in the police/military will not be given a carta blanca, to my knowledge.
5. A plane ticket
The carta blanca is only valid for a certain period of time, so must be co-ordinated with the tourist visa and plane ticket.
What do you need to go and get married in cuba?
1. An original letter of freedom from a legal entitiy in your country, along with an official spanish translation
2. An original birth certificate, along with an official spanish translation
Getting married in cuba is not difficult or expensive - the process is performed in the local legal office and costs a few hundred pesos (dollars), from memory. If you are frustrated in your attempts to get her into your country (particularly in obtaining a tourist or fiance visa) then getting married in cuba may help.