Bismihi ta'ala
Knowledge precedes everything, especially if it is Ilahi knowledge, studying about your religion and learning the 'Ulum of Ahlul Bayt (a.s.).
Studying Hawzah is free of charge, and if for whatever reason a certain institute that offers Hawzah studies charge a fee, they are usually a bare minimum which any person would generally be able to pay.
Should your plan be to travel to Qom or Najaf to study Hawzah, you will only need to pay for the air ticket, and basic expenses to establish yourself there. The Hawzah will then give you some monthly wages.
This could eat into your budget you have allocated for marriage, but if you have become acquainted with Islam, you will know that the process of getting married should also be cheap and reasonable. By avoiding excessive things, you will also be able to get happily married.
Therefore, I do not see any of the two to be an obstacle, or affect the other, as long as you are making the correct choices. You do not have to choose one over the other, but rather pursue both at once.
With your tawakkul on Allah ta'ala, and sincere intentions, and dua, you will successfully accomplish both, in shaa Allah.
With prayers for your success.
