This can sometimes be a difficult situation to navigate among Muslims who handle marriage through interactions between families.
In this situation, you will most likely meet your prospective husband outside of the circle of your own family. (For example, daily life, socializing, Islamic groups or events, online)
In that case, the role of your family here is ethical and social. A prospective husband should make an effort get to know your family and be respectful towards them. If your father were alive, it would be respectful and good form for him to seek your father's blessing for the marriage.
Of course, if your family is hostile towards Islam, or there are other issues, it may be that there will be no extensive relationship between him and them.
However, if a prospective husband does not want to meet your family at all, or is disrespectful, that is a red flag.
As for actual wedding arrangements, or who will pay for a wedding, this is something you, your prospective husband, and your families will have to sort out.
Sometimes, weddings can be a challenge for converts, especially in a marriage between a convert woman and a born-Muslim man. It can be awkward if the born-Muslim brings a large extended family to celebrate, and the convert seems alone. Conversely, the two families may disagree about which wedding customs are important to them.
On the other hand, in a marriage between two converts (who both do not come from Muslim cultures), it can be difficult to decide how to celebrate, since there is no cultural precedent for Muslim weddings.
Some converts sidestep this by skipping a wedding altogether, but many people regret this over time, so it is good to have a suitable wedding - even if it is simple and inexpensive - which is in line with both of your financial and social circumstances. A mosque wedding may also be an option, since it is both public and inexpensive. If the man does not want to have any wedding at all, that is also a red flag.