How to display current dropdown option as first option

The order of dropdown selections won’t change. However, if the user has selected an option, that option should be what is selected when they view their profile.

When i go to my user-profile page, it only shows 2
<li> links, to change my profile info and reset my password, not what my current user info is.

Sorry – I thought your question was about the order in which the dropdown items display.

The profile you are referring to can be customized in a couple different ways.

There is a filter hook wpmem_member_links that allows you to filter the HTML that displays. (These are the
<li> items you mentioned.) You can use the filter to add to the HTML that displays here or change it (although in this case I would say be careful changing it because you need the links to the update profile and update password forms).

If what you want is to display user profile information on this screen, you can use a combination of shortcodes for this. I would probably do something like this:

[wp-members page=user-profile]
[wpmem_logged_in]
Your Current User Info:
Some Field: [wpmem_field field=some_field_name]
Some Other Field: [wpmem_field field=some_field_name]
You can edit this information by <a href="https://yoursite.com/this-page/?a=edit">updating your registration info</a>.
[/wpmem_logged_in]