can’t say at all what will happen in your case, each marriage situation is unique. In general the time sequence is this: the first marriage to be contracted is investigated first, as it is still presumed valid, and any marriage contracted later is presumed to be invalid. If the first marriage is found to be invalid a decree of nullity is issued. If there were intervening marriages that have since broken down, they would be investigated in order.
Once it is determined neither party is at this time validly married to anyone else, they are free to marry again, or if they have already contracted a civil marriage, to have that bond convalidated (assuming all the conditions for validity are present at this time, both parties are free to marry, and there was no condition attached to the annulment finding). There will be some marriage preparation involved, addressed to your situation (how long you have been together, whether you have children, whether either party is non-Catholic etc.) it would not be exactly the same as it would for a young engaged couple, for instance, it would respect your own needs.
If either party in the current marriage is not Catholic and desires now to come into full communion with the Catholic Church, the marriage situation must first be resolved before he or she may be confirmed (or baptized, if that never happened) and receive holy communion. It will be the best judgement of the pastor if you will be invited to participate in a preparation class for sacraments, or RCIA, before the marriage issue is settled. There are different issues and situations involved here as well, too many to discuss with any relevance on this forum as regards to a specific case.
Welcome home, and know this, no matter how long it takes, if this is where you belong you will be home in God’s good time, even when it seems the hurdles never end, every test makes your faith stronger. The submission to the will of God, expressed through the laws of the Church, is inherent to and necessary part of the conversion process.
Some examples if various issues that arise: since your wife is Catholic she is bound now by Catholic law on marriage, whereas you would become bound only when you are baptized. It may transpire, it has happened before, where the party in RCIA never did actually decide to accept baptism, in any case the Catholic spouse still has to bring her situation in line with Church law on marriage so she can return to the sacraments. She may also want to learn more about her own faith, and participate with her non-Catholic spouse in the RCIA or confirmation class. There also differences depending on whether or not the person coming into the Church has been baptized, and sometimes children of the marriage also need to be prepared for sacraments.
It is very common here to celebrate marriage convalidations during the day or week before Easter, or date of confirmation, have candidates come to the sacrament of confession, and then come to the initiation sacraments. Many parishes have the weddings during Holy Week. We had two weddings on Saturday evening the vigil of Pentecost, the candidates then made their confession after Mass, and were confirmed with the bishop the following day. I have seen some parishes where the weddings are right before or even part of the Easter Vigil. That is more a question of logistics and local custom and that timing will be up to the pastor.
There will usually be someone like me in charge of making sure paperwork is in order and everyone is prepared properly for all sacraments received, to handle the details.
One thing is always the same, the celebration of these sacraments opens up channels of amazing life-changing grace for these individuals and families.
